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Introduction To Modern Finsler Geometry
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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.
Book Synopsis Introduction to Modern Finsler Geometry by : Yibing Shen
Download or read book Introduction to Modern Finsler Geometry written by Yibing Shen and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Synopsis An Introduction to Riemann-Finsler Geometry by : D. Bao
Download or read book An Introduction to Riemann-Finsler Geometry written by D. Bao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the elementary but essential problems in Riemann-Finsler Geometry, which include a repertoire of rigidity and comparison theorems, and an array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. "This book offers the most modern treatment of the topic ..." EMS Newsletter.
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. Contents: Finsler Spaces; Finsler m Spaces; Co-Area Formula; Isoperimetric Inequalities; Geodesics and Connection; Riemann Curvature; Non-Riemannian Curvatures; Structure Equations; Finsler Spaces of Constant Curvature; Second Variation Formula; Geodesics and Exponential Map; Conjugate Radius and Injectivity Radius; Basic Comparison Theorems; Geometry of Hypersurfaces; Geometry of Metric Spheres; Volume Comparison Theorems; Morse Theory of Loop Spaces; Vanishing Theorems for Homotopy Groups; Spaces of Finsler Spaces. Readership: Graduate students and researchers in geometry and physics.
Book Synopsis Connections, Sprays and Finsler Structures by : József Szilasi
Download or read book Connections, Sprays and Finsler Structures written by József Szilasi and published by World Scientific Publishing Company. This book was released on 2013-08-16 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to Finsler geometry in the language of present-day mathematics. Through Finsler geometry, it also introduces the reader to other structures and techniques of differential geometry. Prerequisites for reading the book are minimal: undergraduate linear algebra (over the reals) and analysis. The necessary concepts and tools of advanced linear algebra (over modules), point set topology, multivariable calculus and the rudiments of the theory of differential equations are integrated in the text. Basic manifold and bundle theories are treated concisely, carefully and (apart from proofs) in a self-contained manner. The backbone of the book is the detailed and original exposition of tangent bundle geometry, Ehresmann connections and sprays. It turns out that these structures are important not only in their own right and in the foundation of Finsler geometry, but they can be also regarded as the cornerstones of the huge edifice of Differential Geometry. The authors emphasize the conceptual aspects, but carefully elaborate calculative aspects as well (tensor derivations, graded derivations and covariant derivatives). Although they give preference to index-free methods, they also apply the techniques of traditional tensor calculus. Most proofs are elaborated in detail, which makes the book suitable for self-study. Nevertheless, the authors provide for more advanced readers as well by supplying them with adequate material, and the book may also serve as a reference.
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.
Book Synopsis Comparison Finsler Geometry by : Shin-ichi Ohta
Download or read book Comparison Finsler Geometry written by Shin-ichi Ohta and published by Springer Nature. This book was released on 2021-10-09 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds. Generalizing the weighted Ricci curvature into the Finsler setting, the author systematically derives the fundamental geometric and analytic inequalities in the Finsler context. Relying only upon knowledge of differentiable manifolds, this treatment offers an accessible entry point to Finsler geometry for readers new to the area. Divided into three parts, the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields and curvature tensors, variation formulas for arc length, and some classical comparison theorems. Part II goes on to introduce the weighted Ricci curvature, nonlinear Laplacian, and nonlinear heat flow on Finsler manifolds. These tools allow the derivation of the Bochner–Weitzenböck formula and the corresponding Bochner inequality, gradient estimates, Bakry–Ledoux’s Gaussian isoperimetric inequality, and functional inequalities in the Finsler setting. Part III comprises advanced topics: a generalization of the classical Cheeger–Gromoll splitting theorem, the curvature-dimension condition, and the needle decomposition. Throughout, geometric descriptions illuminate the intuition behind the results, while exercises provide opportunities for active engagement. Comparison Finsler Geometry offers an ideal gateway to the study of Finsler manifolds for graduate students and researchers. Knowledge of differentiable manifold theory is assumed, along with the fundamentals of functional analysis. Familiarity with Riemannian geometry is not required, though readers with a background in the area will find their insights are readily transferrable.
Download or read book Applied Differential Geometry written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics by : Molin Ge
Download or read book Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics written by Molin Ge and published by World Scientific. This book was released on 2014-03-18 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers in memory of Gu Chaohao on the subjects of Differential Geometry, Partial Differential Equations and Mathematical Physics that Gu Chaohao made great contributions to with all his intelligence during his lifetime. All contributors to this book are close friends, colleagues and students of Gu Chaohao. They are all excellent experts among whom there are 9 members of the Chinese Academy of Sciences. Therefore this book will provide some important information on the frontiers of the related subjects. Contents:A Profile of the Late Professor Gu Chaohao (Tatsien Li)List of Publications of Gu ChaohaoIn Memory of Professor Gu Chaohao (Xiaqi Ding)In Memory of Professor Gu Chaohao (Gongqing Zhang (Kung-Ching Chang))Stability of E-H Mach Configuration in Pseudo-Steady Compressible Flow (Shuxing Chen)Incompressible Viscous Fluid Flows with Slip Boundary Conditions and Their Numerical Simulations (Ben-yu Guo)Global Existence and Uniqueness of the Solution for the Generalized Schrödinger-KdV System (Boling Guo, Bolin Ma & Jingjun Zhang)Anomaly Cancellation and Modularity (Fei Han, Kefeng Liu & Weiping Zhang)On Interior Estimates for Mean Curvature of Convex Surfaces in R3 and Its Applications (Jiaxing Hong)Geometric Invariant Theory of the Space — A Modern Approach to Solid Geometry (Wu-Yi Hsiang)Optimal Convergence Rate of the Binomial Tree Scheme for American Options and Their Free Boundaries (Lishang Jiang & Jin Liang)Rademacher Φ Function, Jacobi Symbols, Quantum and Classical Invariants of Lens Spaces (Bang-He Li & Tian-Jun Li)Historical Review on the Roles of Mathematics in the Study of Aerodynamics (Jiachun Li)Toward Chern–Simons Theory of Complexes on Calabi–Yau Threefolds (Jun Li)Exact Boundary Synchronization for a Coupled System of Wave Equations (Tatsien Li)Scaling Limit for Compressible Viscoelastic Fluids (Xianpeng Hu & Fang-Hua Lin)Uniqueness Modulo Reduction of Bergman Meromorphic Compactifications of Canonically Embeddable Bergman Manifolds (Ngaiming Mok)The Application of Conditional Nonlinear Optimal Perturbation to Targeted Observations for Tropical Cyclone Prediction (Mu Mu, Feifan Zhou, Xiaohao Qin & Boyu Chen)Isometric Immersions in Minkowski Spaces (Yi-Bing Shen)Remarks on Volume Growth for Minimal Graphs in Higher Codimension (Yuanlong Xin)Separation of Variables for the Lax Pair of the Bogomolny Equation in 2+1 Dimensional Anti-de Sitter Space-Time (Zi-Xiang Zhou) Readership: Mathematicians and advanced graduate students in mathematics. Key Features:In memory of the highly distinguished mathematician Gu ChaohaoThe contributors are excellent experts, including 9 members of the CASProvides some important information on Differential Geometry, Partial Differential Equations, Mathematical Physics, etcKeywords:Differential Geometry;Partial Differential Equations;Mathematical Physics
Book Synopsis Riemannian Geometry by : Isaac Chavel
Download or read book Riemannian Geometry written by Isaac Chavel and published by Cambridge University Press. This book was released on 1995-01-27 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to Riemannian geometry, the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and those new notions and ideas motivated by curvature itself. Isoperimetric inequalities--the interplay of curvature with volume of sets and the areas of their boundaries--is reviewed along with other specialized classical topics. A number of completely new themes are created by curvature: they include local versus global geometric properties, that is, the interaction of microscopic behavior of the geometry with the macroscopic structure of the space. Also featured is an ambitious "Notes and Exercises" section for each chapter that will develop and enrich the reader's appetite and appreciation for the subject.
Author :Peter L. Antonelli Publisher :Springer Science & Business Media ISBN 13 :9781402015564 Total Pages :746 pages Book Rating :4.0/5 (155 download)
Book Synopsis Handbook of Finsler geometry. 2 (2003) by : Peter L. Antonelli
Download or read book Handbook of Finsler geometry. 2 (2003) written by Peter L. Antonelli and published by Springer Science & Business Media. This book was released on 2003 with total page 746 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.
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 2013-03-09 with total page 324 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.
Book Synopsis Modern Graph Theory by : Bela Bollobas
Download or read book Modern Graph Theory written by Bela Bollobas and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pure mathematics. Recognising that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory, the book presents a detailed account of newer topics, including Szemerédis Regularity Lemma and its use, Shelahs extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader.
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 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is two-fold. The author aims to show that Finsler geometry is based on the geometry of vertical vector bundles, and gives some applications of Finsler geometry to physics and engineering.
Author :Peter L. Antonelli Publisher :Springer Science & Business Media ISBN 13 :9781402015557 Total Pages :760 pages Book Rating :4.0/5 (155 download)
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.
