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An Introduction to Riemann-Finsler Geometry

An Introduction to Riemann-Finsler Geometry
Catalogue Information
Field name Details
Dewey Class 516
Title An Introduction to Riemann-Finsler Geometry ([EBook]) / by D. Bao, S.-S. Chern, Z. Shen.
Author Bao, David , 1953-
Added Personal Name Chern, Shiing-shen , 1911-2004
Shen, Zhongmin. , 1963-
Other name(s) SpringerLink (Online service)
Publication New York, NY : Springer , 2000.
Physical Details XX, 435 pages : online resource.
Series Graduate texts in mathematics 0072-5285 ; ; 200
ISBN 9781461212683
Summary Note 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.:
Contents note One Finsler Manifolds and Their Curvature -- 1 Finsler Manifolds and the Fundamentals of Minkowski Norms -- 2 The Chern Connection -- 3 Curvature and Schur’s Lemma -- 4 Finsler Surfaces and a Generalized Gauss—Bonnet Theorem -- Two Calculus of Variations and Comparison Theorems -- 5 Variations of Arc Length, Jacobi Fields, the Effect of Curvature -- 6 The Gauss Lemma and the Hopf-Rinow Theorem -- 7 The Index Form and the Bonnet-Myers Theorem -- 8 The Cut and Conjugate Loci, and Synge’s Theorem -- 9 The Cartan-Hadamard Theorem and Rauch’s First Theorem -- Three Special Finsler Spaces over the Reals -- 10 Berwald Spaces and Szabó’s Theorem for Berwald Surfaces -- 11 Randers Spaces and an Elegant Theorem -- 12 Constant Flag Curvature Spaces and Akbar-Zadeh’s Theorem -- 13 Riemannian Manifolds and Two of Hopf’s Theorems -- 14 Minkowski Spaces, the Theorems of Deicke and Brickell.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-1-4612-1268-3
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