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PRINTED BOOKS
Author Bao, David Dai-Wai.

Title An introduction to Riemann-Finsler geometry / D. Bao, S.-S. Chern, Z. Shen.

Published New York ; London : Springer, [2000]
©2000

Copies

Location Call No. Status
 UniM ERC  516.373 BAO    AVAILABLE
Physical description xx, 431 pages : illustrations ; 25 cm.
Series Graduate texts in mathematics ; 200.
Graduate texts in mathematics ; 200.
Bibliography Includes bibliographical references and index.
Contents Part 1 Finsler Manifolds and Their Curvature 1 -- Chapter 1 Finsler Manifolds and the Fundamentals of Minkowski Norms 1 -- Chapter 2 Chern Connection 27 -- Chapter 3 Curvature and Schur's Lemma 49 -- Chapter 4 Finsler Surfaces and a Generalized Gauss-Bonnet Theorem 81 -- Part 2 Calculus of Variations and Comparison Theorems 111 -- Chapter 5 Variations of Arc Length, Jacobi Fields, the Effect of Curvature 111 -- Chapter 6 Gauss Lemma and the Hopf-Rinow Theorem 139 -- Chapter 7 Index Form and the Bonnet-Myers Theorem 173 -- Chapter 8 Cut and Conjugate Loci, and Synge's Theorem 199 -- Chapter 9 Cartan-Hadamard Theorem and Rauch's First Theorem 225 -- Part 3 Special Finsler Spaces over the Reals 257 -- Chapter 10 Berwald Spaces and Szabo's Theorem for Berwald Surfaces 257 -- Chapter 11 Randers Spaces and an Elegant Theorem 281 -- Chapter 12 Constant Flag Curvature Spaces and Akbar-Zadeh's Theorem 311 -- Chapter 13 Riemannian Manifolds and Two of Hopf's Theorems 351 -- Chapter 14 Minkowski Spaces, the Theorems of Deicke and Brickell 383.
Summary In Riemannian geometry, measurements are made with both yardsticks and protractors. These tools are represented by a family of inner-products. In Riemann-Finsler geometry (or Finsler geometry for short), one is in principle equipped with only a family of Minkowski norms. So ardsticks are assigned but protractors are not. With such a limited tool kit, it is natural to wonder just how much geometry one can uncover and describe? It now appears that there is a reasonable answer. Finsler geometry encompasses a solid repertoire of rigidity and comparison theorems, most of them founded upon a fruitful analogue of the sectional curvature. There is also a bewildering array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. This book focuses on the elementary but essential items among these results. Much thought has gone into making the account a teachable one.
Language notes English.
Other author Shen, Zhongmin, 1963-
Chern, Shiing-Shen, 1911-2004.
Subject Geometry, Riemannian.
Finsler spaces.
ISBN 038798948X No price
038798948X (acid-free paper)
038798948X
038798948X (alk. paper)