Graduate Texts in Mathematics

An Introduction to Riemann-Finsler Geometry

Authors: Bao, D., Chern, S.-S., Shen, Z.

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eBook $64.99
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  • ISBN 978-1-4612-1268-3
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Hardcover $84.95
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  • ISBN 978-0-387-98948-8
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Softcover $84.95
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  • ISBN 978-1-4612-7070-6
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About this Textbook

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.

Reviews

"This book offers the most modern treatment of the topic and will attract both graduate students and a broad community of mathematicians from various related fields."
EMS Newsletter, Issue 41, September 2001

Table of contents (14 chapters)

  • Finsler Manifolds and the Fundamentals of Minkowski Norms

    Bao, D. (et al.)

    Pages 1-26

  • The Chern Connection

    Bao, D. (et al.)

    Pages 27-48

  • Curvature and Schur’s Lemma

    Bao, D. (et al.)

    Pages 49-80

  • Finsler Surfaces and a Generalized Gauss-Bonnet Theorem

    Bao, D. (et al.)

    Pages 81-110

  • Variations of Arc Length, Jacobi Fields, the Effect of Curvature

    Bao, D. (et al.)

    Pages 111-138

Buy this book

eBook $64.99
price for USA (gross)
  • ISBN 978-1-4612-1268-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $84.95
price for USA
  • ISBN 978-0-387-98948-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $84.95
price for USA
  • ISBN 978-1-4612-7070-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Riemann-Finsler Geometry
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
200
Copyright
2000
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1268-3
DOI
10.1007/978-1-4612-1268-3
Hardcover ISBN
978-0-387-98948-8
Softcover ISBN
978-1-4612-7070-6
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XX, 435
Topics