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Metric Methods In Finsler Spaces And In The Foundations Of Geometry
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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 Princeton University Press. This book was released on 2016-03-02 with total page 243 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.
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 2001-05-22 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.
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.
Book Synopsis Finsler Geometry, Relativity and Gauge Theories by : G.S. Asanov
Download or read book Finsler Geometry, Relativity and Gauge Theories written by G.S. Asanov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: The methods of differential geometry have been so completely merged nowadays with physical concepts that general relativity may well be considered to be a physical theory of the geometrical properties of space-time. The general relativity principles together with the recent development of Finsler geometry as a metric generalization of Riemannian geometry justify the attempt to systematize the basic techniques for extending general relativity on the basis of Finsler geometry. It is this endeavour that forms the subject matter of the present book. Our exposition reveals the remarkable fact that the Finslerian approach is automatically permeated with the idea of the unification of the geometrical space-time picture with gauge field theory - a circumstance that we try our best to elucidate in this book. The book has been written in such a way that the reader acquainted with the methods of tensor calculus and linear algebra at the graduate level can use it as a manual of Finslerian techniques orientable to applications in several fields. The problems attached to the chapters are also intended to serve this purpose. This notwithstanding, whenever we touch upon the Finslerian refinement or generalization of physical concepts, we assume that the reader is acquainted with these concepts at least at the level of the standard textbooks, to which we refer him or her.
Book Synopsis The Differential Geometry of Finsler Spaces by : Hanno Rund
Download or read book The Differential Geometry of Finsler Spaces written by Hanno Rund and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph is motivated by two distinct aims. Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential geometry. Secondly, it is hoped that this monograph may serve also as an introduction to a branch of differential geometry which is closely related to various topics in theoretical physics, notably analytical dynamics and geometrical optics. With this second object in mind, an attempt has been made to describe the basic aspects of the theory in some detail - even at the expense of conciseness - while in the more specialised sections of the later chapters, which might be of interest chiefly to the specialist, a more succinct style has been adopted. The fact that there exist several fundamentally different points of view with regard to Finsler geometry has rendered the task of writing a coherent account a rather difficult one. This remark is relevant not only to the development of the subject on the basis of the tensor calculus, but is applicable in an even wider sense. The extensive work of H. BUSEMANN has opened up new avenues of approach to Finsler geometry which are independent of the methods of classical tensor analysis. In the latter sense, therefore, a full description of this approach does not fall within the scope of this treatise, although its fundamental l significance cannot be doubted.
Book Synopsis The Geometry of Geodesics by : Herbert Busemann
Download or read book The Geometry of Geodesics written by Herbert Busemann and published by Courier Corporation. This book was released on 2012-07-12 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
Book Synopsis Pure Metric Geometry by : Anton Petrunin
Download or read book Pure Metric Geometry written by Anton Petrunin and published by Springer Nature. This book was released on 2023-12-23 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introductory asset for learning metric geometry by delivering an in-depth examination of key constructions and providing an analysis of universal spaces, injective spaces, the Gromov-Hausdorff convergence, and ultralimits. This book illustrates basic examples of domestic affairs of metric spaces, this includes Alexandrov geometry, geometric group theory, metric-measure spaces and optimal transport. Researchers in metric geometry will find this book appealing and helpful, in addition to graduate students in mathematics, and advanced undergraduate students in need of an introduction to metric geometry. Any previous knowledge of classical geometry, differential geometry, topology, and real analysis will be useful in understanding the presented topics.
Book Synopsis Metric Spaces, Convexity and Nonpositive Curvature by : Athanase Papadopoulos
Download or read book Metric Spaces, Convexity and Nonpositive Curvature written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2005 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Metric Spaces of Non-Positive Curvature by : Martin R. Bridson
Download or read book Metric Spaces of Non-Positive Curvature written by Martin R. Bridson and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects is developed in a manner accessible to anyone familiar with the rudiments of topology and group theory: non-trivial theorems are proved by concatenating elementary geometric arguments, and many examples are given. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds. More specialized topics, such as complexes of groups, are covered in Part III.
Book Synopsis The Global Structure of Visual Space by : Tarow Indow
Download or read book The Global Structure of Visual Space written by Tarow Indow and published by World Scientific. This book was released on 2004 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation - Most studies of visual perception, such as illusion, perception of solid objects and colors, etc., are concerned with local phenomena in this visual space. In contrast, this book focuses on the global structure inherent in our visual space- Developments in the Structure of Visual Space is summarized in the book. Moreover, the idea is discussed with regard to our visual space under more natural conditions- The book will be of interest to scientists and engineers in various fields who are interested in human vision and to artists who are interested in the scientific understanding of seeing- This book includes many illustrations- All mathematical tools are explained from the beginning, so it is still readable to those who are not familiar with Riemannian geometry- The backgrounds of experimentation are described in detail, so it is also readable to those who are unfamiliar with experiments on visual perception
Book Synopsis Surveys in Geometry II by : Athanase Papadopoulos
Download or read book Surveys in Geometry II written by Athanase Papadopoulos and published by Springer Nature. This book was released on with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry in History written by S. G. Dani and published by Springer Nature. This book was released on 2019-10-18 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.
Book Synopsis Handbook of the History and Philosophy of Mathematical Practice by : Bharath Sriraman
Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Global Lorentzian Geometry by : John K. Beem
Download or read book Global Lorentzian Geometry written by John K. Beem and published by Routledge. This book was released on 2017-09-29 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.
Book Synopsis Canadian Journal of Mathematics by :
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1949 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Canadian Journal of Mathematics by :
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1952 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Selected Works I by : Herbert Busemann
Download or read book Selected Works I written by Herbert Busemann and published by Springer. This book was released on 2018-06-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a two-volume collection presenting the selected works of Herbert Busemann, one of the leading geometers of the twentieth century and one of the main founders of metric geometry, convexity theory and convexity in metric spaces. Busemann also did substantial work (probably the most important) on Hilbert’s Problem IV. These collected works include Busemann’s most important published articles on these topics. Volume I of the collection features Busemann’s papers on the foundations of geodesic spaces and on the metric geometry of Finsler spaces. Volume II includes Busemann’s papers on convexity and integral geometry, on Hilbert’s Problem IV, and other papers on miscellaneous subjects. Each volume offers biographical documents and introductory essays on Busemann’s work, documents from his correspondence and introductory essays written by leading specialists on Busemann’s work. They are a valuable resource for researchers in synthetic and metric geometry, convexity theory and the foundations of geometry.
