An Introduction to Riemann-Finsler Geometry (Graduate Texts in Mathematics) | 
 enlarge | Authors: David Dai-wai Bao, Shiing-shen Chern, Zhongmin Shen
Publisher: Springer
Category: Book
List Price: $74.95
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Rating:  1 reviews
Sales Rank: 1475715
Media: Hardcover
Edition: 1
Pages: 431
Number Of Items: 1
Shipping Weight (lbs): 1.9
Dimensions (in): 9.6 x 6.5 x 1.2
ISBN: 038798948X
Dewey Decimal Number: 516.373
EAN: 9780387989488
Publication Date: March 17, 2000
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Product Description
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.
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| Customer Reviews:
Mainly for experts in Finsler geometry March 13, 2005
Dr. Oliver Strebel (Berlin, Deutschland)
2 out of 3 found this review helpful
The authors claim to turn the subject of Finsler geometry with this book
into a more teachable one and to have a candid style of writing.
This is definitly true for the first 50 pages, where the concepts of
Finsler geometry are very well explained and the exercises
are manageable and perfectly interrelated with the text.
Then the Chern connection and the curvature tensor of Finsler geometry
drop out of the heaven without any explanation of the ideas leading to these
constructions. So one has to derive them alone. In doing so older
texts on Finsler geometry like the Grundlehren text of Rund are more
helpful than this volume.
But the book was apparently prepared with great care. The layout must be called
beautyful and it really facilitates reading this book. Many references
to the literature and classical papers of the subject are included. So beginners,
which want to get a first aquaintance in Finsler geometry, find at least some help.
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