# An Introduction to Riemann-Finsler Geometry

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

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

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.

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.

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

- 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
- About this book