Lectures On Finsler Geometry

Author : Zhongmin Shen
Publisher : World Scientific
Page : 323 pages
File Size : 44,5 Mb
Release : 2001
Category : Mathematics
ISBN : 9789810245306

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Lectures on Finsler Geometry by Zhongmin Shen Pdf

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.

Author : S S Chern,W H Chen,K S Lam
Publisher : World Scientific Publishing Company
Page : 368 pages
File Size : 46,6 Mb
Release : 1999-11-30
Category : Mathematics
ISBN : 9789813102989

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Lectures on Differential Geometry by S S Chern,W H Chen,K S Lam Pdf

This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.

Author : Shiing-Shen Chern,Weihuan Chen,Kai Shue Lam
Publisher : World Scientific
Page : 370 pages
File Size : 53,9 Mb
Release : 1999
Category : Mathematics
ISBN : 9810241828

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Lectures on Differential Geometry by Shiing-Shen Chern,Weihuan Chen,Kai Shue Lam Pdf

This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.

Author : Xiaohuan Mo
Publisher : World Scientific
Page : 130 pages
File Size : 54,9 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812773715

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An Introduction to Finsler Geometry by Xiaohuan Mo Pdf

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.

Author : Yi-Bing Shen,Zhongmin Shen
Publisher : World Scientific Publishing Company
Page : 408 pages
File Size : 48,5 Mb
Release : 2016-02-25
Category : Mathematics
ISBN : 9789814704922

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Introduction to Modern Finsler Geometry by Yi-Bing Shen,Zhongmin Shen Pdf

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.

Author : David Dai-Wai Bao,Shiing-Shen Chern,Zhongmin Shen
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 47,7 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805077

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Finsler Geometry by David Dai-Wai Bao,Shiing-Shen Chern,Zhongmin Shen Pdf

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.

Author : Peter L. Antonelli
Publisher : Springer Science & Business Media
Page : 746 pages
File Size : 53,9 Mb
Release : 2003
Category : Mathematics
ISBN : 1402015569

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Handbook of Finsler geometry. 2 (2003) by Peter L. Antonelli Pdf

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.

Author : David Dai-Wai Bao
Publisher : Cambridge University Press
Page : 384 pages
File Size : 55,5 Mb
Release : 2004-11
Category : Mathematics
ISBN : 0521831814

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A Sampler of Riemann-Finsler Geometry by David Dai-Wai Bao Pdf

These expository accounts treat issues related to volume, geodesics, curvature and mathematical biology, with instructive examples.

Author : Shin-ichi Ohta
Publisher : Springer Nature
Page : 324 pages
File Size : 52,8 Mb
Release : 2021-10-09
Category : Mathematics
ISBN : 9783030806507

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Comparison Finsler Geometry by Shin-ichi Ohta Pdf

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.

Author : Shiing-Shen Chern,Zhongmin Shen
Publisher : World Scientific
Page : 206 pages
File Size : 49,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812383570

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Riemann-Finsler Geometry by Shiing-Shen Chern,Zhongmin Shen Pdf

Riemann-Finsler geometry is a subject that concerns manifolds with Finsler metrics, including Riemannian metrics. It has applications in many fields of the natural sciences. Curvature is the central concept in Riemann-Finsler geometry. This invaluable textbook presents detailed discussions on important curvatures such the Cartan torsion, the S-curvature, the Landsberg curvature and the Riemann curvature. It also deals with Finsler metrics with special curvature or geodesic properties, such as projectively flat Finsler metrics, Berwald metrics, Finsler metrics of scalar curvature or isotropic S-curvature, etc. Instructive examples are given in abundance, for further description of some important geometric concepts. The text includes the most recent results, although many of the problems discussed are classical. Graduate students and researchers in differential geometry.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 138 pages
File Size : 54,5 Mb
Release : 1977-12-31
Category : Mathematics
ISBN : 082189546X

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20 Lectures Delivered at the International Congress of Mathematicians in Vancouver, 1974 by Anonim Pdf

Author : Xinyue Cheng,Zhongmin Shen
Publisher : Springer Science & Business Media
Page : 150 pages
File Size : 47,9 Mb
Release : 2013-01-29
Category : Mathematics
ISBN : 9783642248887

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Finsler Geometry by Xinyue Cheng,Zhongmin Shen Pdf

"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.

Author : Giovanni Falcone
Publisher : Springer
Page : 361 pages
File Size : 51,8 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9783319621814

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Lie Groups, Differential Equations, and Geometry by Giovanni Falcone Pdf

This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.

Author : András Prékopa,Emil Molnár
Publisher : Springer Science & Business Media
Page : 497 pages
File Size : 41,6 Mb
Release : 2006-06-03
Category : Mathematics
ISBN : 9780387295558

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Non-Euclidean Geometries by András Prékopa,Emil Molnár Pdf

"From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.

Author : Yibing Shen,Zhongmin Shen,Shing-Tung Yau
Publisher : Unknown
Page : 336 pages
File Size : 54,5 Mb
Release : 2012
Category : Finsler spaces
ISBN : 157146249X

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Differential Geometry by Yibing Shen,Zhongmin Shen,Shing-Tung Yau Pdf

The editors dedicate this volume to the late S.–S. Chern, one of the great mathematicians of the twentieth century, and a leader in the field of differential geometry. Chern made seminal advances in areas such as web geometry, integral geometry, complex geometry, Riemannian geometry, and Finsler geometry. He is well-known for the Chern-Simons theory, the Chern-Weil theory, and Chern classes. His brilliant research and teaching have exerted a deep and lasting influence on mathematics.

Presented herein are survey papers by mathematicians from around the world, particularly from China, who review the present state of the areas in which Chern worked, and discuss the various directions which those fields will take in the future. This collection contains valuable information useful to graduate students and researchers.