The Geometry Of Finsler Spaces An Approach Via Special Finsler Metric

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The Geometry of Finsler Spaces: an Approach Via Special Finsler Metric

Author : Sruthy Baby
Publisher :
ISBN 13 : 9781701139145
Total Pages : 149 pages
Book Rating : 4.1/5 (391 download)

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Book Synopsis The Geometry of Finsler Spaces: an Approach Via Special Finsler Metric by : Sruthy Baby

Download or read book The Geometry of Finsler Spaces: an Approach Via Special Finsler Metric written by Sruthy Baby and published by . This book was released on 2019-10-20 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finsler geometry is Riemannian geometry without the restriction that the line element be quadratic. It has applications in many field of natural science especially in mechanics, gravitational theory, electromagnetism, information geometry etc. This book presents some work done by the author on the theory of projective change between two Finsler spaces, Conformal change of Douglas space with special Finsler metric, Nonholonomic Frames for Finsler space with special ( α, β) metric, Reversible geodesics of Finslerian space, Complex Finsler space, Rander -conformal change of Finsler spaces, and the curvature properties of Finsler space. The chapters included in this book contains fundamental topic of modern Riemann Finsler geometry, including the notion of curvature, projectively flat metrics, dually flat metrics which are interesting not only for specialists in Finsler Geometry, but for researchers in Riemann Geometry or other field of differential geometry.The book provides readers with essential findings on a special type of Finsler metric, which can be considered as a generalization of Randers metric and square metric.The text includes the most recent topics in Finsler Geometry like Reversible geodesics of Finsler space, R-Complex Finsler space and transformation on Finsler metric.This book shall be of benefit to students in the field of Differential geometry, and will be of interest to physicists and mathematical biologists.

Finsler Geometry

Author : Xinyue Cheng
Publisher : Springer Science & Business Media
ISBN 13 : 3642248888
Total Pages : 149 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Finsler Geometry by : Xinyue Cheng

Download or read book Finsler Geometry written by Xinyue Cheng and published by Springer Science & Business Media. This book was released on 2013-01-29 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Finsler Geometry: An Approach via Randers Spaces" exclusively deals with a special class of Finsler metrics -- Randers metrics, which are defined as the sum of a Riemannian metric and a 1-form. Randers metrics derive from the research on General Relativity Theory and have been applied in many areas of the natural sciences. They can also be naturally deduced as the solution of the Zermelo navigation problem. The book provides readers not only with essential findings on Randers metrics but also the core ideas and methods which are useful in Finsler geometry. It will be of significant interest to researchers and practitioners working in Finsler geometry, even in differential geometry or related natural fields. Xinyue Cheng is a Professor at the School of Mathematics and Statistics of Chongqing University of Technology, China. Zhongmin Shen is a Professor at the Department of Mathematical Sciences of Indiana University Purdue University, USA.

Homogeneous Finsler Spaces

Author : Shaoqiang Deng
Publisher : Springer Science & Business Media
ISBN 13 : 1461442443
Total Pages : 250 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Homogeneous Finsler Spaces by : Shaoqiang Deng

Download or read book Homogeneous Finsler Spaces written by Shaoqiang Deng and published by Springer Science & Business Media. This book was released on 2012-08-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homogeneous Finsler Spaces is the first book to emphasize the relationship between Lie groups and Finsler geometry, and the first to show the validity in using Lie theory for the study of Finsler geometry problems. This book contains a series of new results obtained by the author and collaborators during the last decade. The topic of Finsler geometry has developed rapidly in recent years. One of the main reasons for its surge in development is its use in many scientific fields, such as general relativity, mathematical biology, and phycology (study of algae). This monograph introduces the most recent developments in the study of Lie groups and homogeneous Finsler spaces, leading the reader to directions for further development. The book contains many interesting results such as a Finslerian version of the Myers-Steenrod Theorem, the existence theorem for invariant non-Riemannian Finsler metrics on coset spaces, the Berwaldian characterization of globally symmetric Finsler spaces, the construction of examples of reversible non-Berwaldian Finsler spaces with vanishing S-curvature, and a classification of homogeneous Randers spaces with isotropic S-curvature and positive flag curvature. Readers with some background in Lie theory or differential geometry can quickly begin studying problems concerning Lie groups and Finsler geometry.

Lectures on Finsler Geometry

Author : Zhongmin Shen
Publisher : World Scientific
ISBN 13 : 9810245300
Total Pages : 323 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Lectures on Finsler Geometry by : Zhongmin Shen

Download or read book Lectures on Finsler Geometry written by Zhongmin Shen and published by World Scientific. This book was released on 2001 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1854, B Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P Finsler studied the variation problem in regular metric spaces. Around 1926, L Berwald extended Riemann's notion of curvature to regular metric spaces and introduced an important non-Riemannian curvature using his connection for regular metrics. Since then, Finsler geometry has developed steadily. In his Paris address in 1900, D Hilbert formulated 23 problems, the 4th and 23rd problems being in Finsler's category. Finsler geometry has broader applications in many areas of science and will continue to develop through the efforts of many geometers around the world.Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern metric geometry point of view. The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory of regular metric measure spaces and Gromov's Hausdorff convergence theory.

Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8)

Author : Herbert Busemann
Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) by : Herbert Busemann

Download or read book Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) written by Herbert Busemann and published by . This book was released on 1942 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8), will be forthcoming.

Handbook of Finsler geometry. 1 (2003)

Author : Peter L. Antonelli
Publisher : Springer Science & Business Media
ISBN 13 : 9781402015557
Total Pages : 760 pages
Book Rating : 4.0/5 (155 download)

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Book Synopsis Handbook of Finsler geometry. 1 (2003) by : Peter L. Antonelli

Download or read book Handbook of Finsler geometry. 1 (2003) written by Peter L. Antonelli and published by Springer Science & Business Media. This book was released on 2003 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are several mathematical approaches to Finsler Geometry, all of which are contained and expounded in this comprehensive Handbook. The principal bundles pathway to state-of-the-art Finsler Theory is here provided by M. Matsumoto. His is a cornerstone for this set of essays, as are the articles of R. Miron (Lagrange Geometry) and J. Szilasi (Spray and Finsler Geometry). After studying either one of these, the reader will be able to understand the included survey articles on complex manifolds, holonomy, sprays and KCC-theory, symplectic structures, Legendre duality, Hodge theory and Gauss-Bonnet formulas. Finslerian diffusion theory is presented by its founders, P. Antonelli and T. Zastawniak. To help with calculations and conceptualizations, a CD-ROM containing the software package FINSLER, based on MAPLE, is included with the book.

Finsler Geometry

Author : David Dai-Wai Bao
Publisher : American Mathematical Soc.
ISBN 13 : 082180507X
Total Pages : 338 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Finsler Geometry by : David Dai-Wai Bao

Download or read book Finsler Geometry written by David Dai-Wai Bao and published by American Mathematical Soc.. This book was released on 1996 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features proceedings from the 1995 Joint Summer Research Conference on Finsler Geometry, chaired by S. S. Chern and co-chaired by D. Bao and Z. Shen. The editors of this volume have provided comprehensive and informative "capsules" of presentations and technical reports. This was facilitated by classifying the papers into the following 6 separate sections - 3 of which are applied and 3 are pure: * Finsler Geometry over the reals * Complex Finsler geometry * Generalized Finsler metrics * Applications to biology, engineering, and physics * Applications to control theory * Applications to relativistic field theory Each section contains a preface that provides a coherent overview of the topic and includes an outline of the current directions of research and new perspectives. A short list of open problems concludes each contributed paper. A number of photos are featured in the volumes, for example, that of Finsler. In addition, conference participants are also highlighted.

Finsler Metrics - A Global Approach

Author : Marco Abate
Publisher : Springer
ISBN 13 : 354048812X
Total Pages : 185 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Finsler Metrics - A Global Approach by : Marco Abate

Download or read book Finsler Metrics - A Global Approach written by Marco Abate and published by Springer. This book was released on 2006-11-15 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Finsler metrics appear naturally in complex analysis. To develop new tools in this area, the book provides a graduate-level introduction to differential geometry of complex Finsler metrics. After reviewing real Finsler geometry stressing global results, complex Finsler geometry is presented introducing connections, Kählerianity, geodesics, curvature. Finally global geometry and complex Monge-Ampère equations are discussed for Finsler manifolds with constant holomorphic curvature, which are important in geometric function theory. Following E. Cartan, S.S. Chern and S. Kobayashi, the global approach carries the full strength of hermitian geometry of vector bundles avoiding cumbersome computations, and thus fosters applications in other fields.

Introduction to Modern Finsler Geometry

Author : Yi-Bing Shen
Publisher : World Scientific Publishing Company
ISBN 13 : 981470492X
Total Pages : 408 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Introduction to Modern Finsler Geometry by : Yi-Bing Shen

Download or read book Introduction to Modern Finsler Geometry written by Yi-Bing Shen and published by World Scientific Publishing Company. This book was released on 2016-02-25 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds. In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.

An Introduction to Finsler Geometry

Author : Xiaohuan Mo
Publisher : World Scientific
ISBN 13 : 9812567933
Total Pages : 130 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis An Introduction to Finsler Geometry by : Xiaohuan Mo

Download or read book An Introduction to Finsler Geometry written by Xiaohuan Mo and published by World Scientific. This book was released on 2006 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory book uses the moving frame as a tool and develops Finsler geometry on the basis of the Chern connection and the projective sphere bundle. It systematically introduces three classes of geometrical invariants on Finsler manifolds and their intrinsic relations, analyzes local and global results from classic and modern Finsler geometry, and gives non-trivial examples of Finsler manifolds satisfying different curvature conditions. Book jacket.

The Geometry of Spherically Symmetric Finsler Manifolds

Author : Enli Guo
Publisher : Springer
ISBN 13 : 9811315981
Total Pages : 154 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis The Geometry of Spherically Symmetric Finsler Manifolds by : Enli Guo

Download or read book The Geometry of Spherically Symmetric Finsler Manifolds written by Enli Guo and published by Springer. This book was released on 2018-09-21 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents properties, examples, rigidity theorems and classification results of such Finsler metrics. In particular, this book introduces how to investigate spherically symmetric Finsler geometry using ODE or PDE methods. Spherically symmetric Finsler geometry is a subject that concerns domains in R^n with spherically symmetric metrics. Recently, a significant progress has been made in studying Riemannian-Finsler geometry. However, constructing nice examples of Finsler metrics turn out to be very difficult. In spherically symmetric Finsler geometry, we find many nice examples with special curvature properties using PDE technique. The studying of spherically symmetric geometry shows closed relation among geometry, group and equation.

The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology

Author : P.L. Antonelli
Publisher : Springer Science & Business Media
ISBN 13 : 9780792325772
Total Pages : 338 pages
Book Rating : 4.3/5 (257 download)

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Book Synopsis The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology by : P.L. Antonelli

Download or read book The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology written by P.L. Antonelli and published by Springer Science & Business Media. This book was released on 1993-10-31 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book has been written by two mathematicians and one physicist: a pure mathematician specializing in Finsler geometry (Makoto Matsumoto), one working in mathematical biology (Peter Antonelli), and a mathematical physicist specializing in information thermodynamics (Roman Ingarden). The main purpose of this book is to present the principles and methods of sprays (path spaces) and Finsler spaces together with examples of applications to physical and life sciences. It is our aim to write an introductory book on Finsler geometry and its applications at a fairly advanced level. It is intended especially for graduate students in pure mathemat ics, science and applied mathematics, but should be also of interest to those pure "Finslerists" who would like to see their subject applied. After more than 70 years of relatively slow development Finsler geometry is now a modern subject with a large body of theorems and techniques and has math ematical content comparable to any field of modern differential geometry. The time has come to say this in full voice, against those who have thought Finsler geometry, because of its computational complexity, is only of marginal interest and with prac tically no interesting applications. Contrary to these outdated fossilized opinions, we believe "the world is Finslerian" in a true sense and we will try to show this in our application in thermodynamics, optics, ecology, evolution and developmental biology. On the other hand, while the complexity of the subject has not disappeared, the modern bundle theoretic approach has increased greatly its understandability.

Finsler Geometry and Applications

Author : Aurel Bejancu
Publisher :
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis Finsler Geometry and Applications by : Aurel Bejancu

Download or read book Finsler Geometry and Applications written by Aurel Bejancu and published by . This book was released on 1990 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Finslerian Geometries

Author : P.L. Antonelli
Publisher : Springer Science & Business Media
ISBN 13 : 9401142351
Total Pages : 305 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Finslerian Geometries by : P.L. Antonelli

Download or read book Finslerian Geometries written by P.L. Antonelli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Finsler and Lagrange Geometry and its Applications: A Meeting of Minds, took place August 13-20, 1998 at the University of Alberta in Edmonton, Canada. The main objective of this meeting was to help acquaint North American geometers with the extensive modern literature on Finsler geometry and Lagrange geometry of the Japanese and European schools, each with its own venerable history, on the one hand, and to communicate recent advances in stochastic theory and Hodge theory for Finsler manifolds by the younger North American school, on the other. The intent was to bring together practitioners of these schools of thought in a Canadian venue where there would be ample opportunity to exchange information and have cordial personal interactions. The present set of refereed papers begins ·with the Pedagogical Sec tion I, where introductory and brief survey articles are presented, one from the Japanese School and two from the European School (Romania and Hungary). These have been prepared for non-experts with the intent of explaining basic points of view. The Section III is the main body of work. It is arranged in alphabetical order, by author. Section II gives a brief account of each of these contribu tions with a short reference list at the end. More extensive references are given in the individual articles.

Complex Spaces in Finsler, Lagrange and Hamilton Geometries

Author : Gheorghe Munteanu
Publisher : Springer Science & Business Media
ISBN 13 : 9781402022050
Total Pages : 288 pages
Book Rating : 4.0/5 (22 download)

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Book Synopsis Complex Spaces in Finsler, Lagrange and Hamilton Geometries by : Gheorghe Munteanu

Download or read book Complex Spaces in Finsler, Lagrange and Hamilton Geometries written by Gheorghe Munteanu and published by Springer Science & Business Media. This book was released on 2004-07-20 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the most recent advances in complex Finsler geometry and related geometries: the geometry of complex Lagrange, Hamilton and Cartan Spaces. The last three spaces were initially introduced to and have been investigated by the author of the present volume over the past several years. This book will acquaint the reader with: - a survey of some basic results from complex manifolds and the complex vector bundles theory, - the geometry of holomorphic tangent bundles, - an analysis of the main results in complex Finsler geometry, - a study of the geometry of complex Lagrange and generalized Lagrange Spaces. Of special interest are their holomorphic subspaces, - the construction of the complex Hamilton geometry, - the complex Finsler vector bundles. Audience: Geometers, complex analysts, and physicists in quantum field theory and in theoretical mechanics will find this book of interest. The volume can be also used as a supplementary graduate text.

Finsler and Lagrange Geometries

Author : Mihai Anastasiei
Publisher : Springer Science & Business Media
ISBN 13 : 9781402013904
Total Pages : 346 pages
Book Rating : 4.0/5 (139 download)

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Book Synopsis Finsler and Lagrange Geometries by : Mihai Anastasiei

Download or read book Finsler and Lagrange Geometries written by Mihai Anastasiei and published by Springer Science & Business Media. This book was released on 2003-07-31 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade several international conferences on Finsler, Lagrange and Hamilton geometries were organized in Bra§ov, Romania (1994), Seattle, USA (1995), Edmonton, Canada (1998), besides the Seminars that periodically are held in Japan and Romania. All these meetings produced important progress in the field and brought forth the appearance of some reference volumes. Along this line, a new International Conference on Finsler and Lagrange Geometry took place August 26-31,2001 at the "Al.I.Cuza" University in Ia§i, Romania. This Conference was organized in the framework of a Memorandum of Un derstanding (1994-2004) between the "Al.I.Cuza" University in Ia§i, Romania and the University of Alberta in Edmonton, Canada. It was especially dedicated to Prof. Dr. Peter Louis Antonelli, the liaison officer in the Memorandum, an untired promoter of Finsler, Lagrange and Hamilton geometries, very close to the Romanian School of Geometry led by Prof. Dr. Radu Miron. The dedica tion wished to mark also the 60th birthday of Prof. Dr. Peter Louis Antonelli. With this occasion a Diploma was given to Professor Dr. Peter Louis Antonelli conferring the title of Honorary Professor granted to him by the Senate of the oldest Romanian University (140 years), the "Al.I.Cuza" University, Ia§i, Roma nia. There were almost fifty participants from Egypt, Greece, Hungary, Japan, Romania, USA. There were scheduled 45 minutes lectures as well as short communications.

Lagrange and Finsler Geometry

Author : P.L. Antonelli
Publisher : Springer Science & Business Media
ISBN 13 : 9401586500
Total Pages : 285 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Lagrange and Finsler Geometry by : P.L. Antonelli

Download or read book Lagrange and Finsler Geometry written by P.L. Antonelli and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The differential geometry of a regular Lagrangian is more involved than that of classical kinetic energy and consequently is far from being Riemannian. Nevertheless, such geometries are playing an increasingly important role in a wide variety of problems in fields ranging from relativistic optics to ecology. The present collection of papers will serve to bring the reader up-to-date on the most recent advances. Subjects treated include higher order Lagrange geometry, the recent theory of -Lagrange manifolds, electromagnetic theory and neurophysiology. Audience: This book is recommended as a (supplementary) text in graduate courses in differential geometry and its applications, and will also be of interest to physicists and mathematical biologists.