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An Introduction to Riemann-Finsler Geometry

  • D. Bao
  • S.-S. Chern
  • Z. Shen

Part of the Graduate Texts in Mathematics book series (GTM, volume 200)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Finsler Manifolds and Their Curvature

    1. D. Bao, S.-S. Chern, Z. Shen
      Pages 1-26
    2. D. Bao, S.-S. Chern, Z. Shen
      Pages 27-48
    3. D. Bao, S.-S. Chern, Z. Shen
      Pages 49-80
    4. D. Bao, S.-S. Chern, Z. Shen
      Pages 81-110
  3. Calculus of Variations and Comparison Theorems

    1. D. Bao, S.-S. Chern, Z. Shen
      Pages 111-138
    2. D. Bao, S.-S. Chern, Z. Shen
      Pages 139-172
    3. D. Bao, S.-S. Chern, Z. Shen
      Pages 173-198
    4. D. Bao, S.-S. Chern, Z. Shen
      Pages 199-224
    5. D. Bao, S.-S. Chern, Z. Shen
      Pages 225-256
  4. Special Finsler Spaces over the Reals

    1. D. Bao, S.-S. Chern, Z. Shen
      Pages 257-280
    2. D. Bao, S.-S. Chern, Z. Shen
      Pages 281-310
    3. D. Bao, S.-S. Chern, Z. Shen
      Pages 311-350
    4. D. Bao, S.-S. Chern, Z. Shen
      Pages 351-382
    5. D. Bao, S.-S. Chern, Z. Shen
      Pages 383-418
  5. Back Matter
    Pages 419-435

About this book

Introduction

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.

Keywords

Calc DEX Jacobi Lemma Natural Riemann-Finsler Geometry Riemannian Geometry Volume calculus calculus of variations constant curvature form theorem tool

Authors and affiliations

  • D. Bao
    • 1
  • S.-S. Chern
    • 2
  • Z. Shen
    • 3
  1. 1.Department of MathematicsUniversity of HoustonUniversity Park, HoustonUSA
  2. 2.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA
  3. 3.Department of Mathematical SciencesIndiana University-Purdue University IndianapolisIndianapolisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1268-3
  • Copyright Information Springer-Verlag New York, Inc. 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7070-6
  • Online ISBN 978-1-4612-1268-3
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site