An Introduction to Riemann-Finsler Geometry (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
435
Utgivningsdatum
2012-10-03
Upplaga
Softcover reprint of the original 1st ed. 2000
Förlag
Springer-Verlag New York Inc.
Medarbetare
Chern, S.-S. / Shen, Z.
Illustrationer
XX, 435 p.
Dimensioner
234 x 156 x 24 mm
Vikt
640 g
Antal komponenter
1
Komponenter
1 Paperback / softback
ISBN
9781461270706

An Introduction to Riemann-Finsler Geometry

av D Bao, S-S Chern, Z Shen
Häftad,  Engelska, 2012-10-03
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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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  • Introduction to Riemann-Finsler Geometry

    Introduction to Riemann-Finsler Geometry

    D Bao, S-S Chern, Z Shen

    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 fa...

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Recensioner i media

"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

Innehållsförteckning

One Finsler Manifolds and Their Curvature.- 1 Finsler Manifolds and the Fundamentals of Minkowski Norms.- 2 The Chern Connection.- 3 Curvature and Schurs Lemma.- 4 Finsler Surfaces and a Generalized GaussBonnet 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 Synges Theorem.- 9 The Cartan-Hadamard Theorem and Rauchs First Theorem.- Three Special Finsler Spaces over the Reals.- 10 Berwald Spaces and Szabs Theorem for Berwald Surfaces.- 11 Randers Spaces and an Elegant Theorem.- 12 Constant Flag Curvature Spaces and Akbar-Zadehs Theorem.- 13 Riemannian Manifolds and Two of Hopfs Theorems.- 14 Minkowski Spaces, the Theorems of Deicke and Brickell.

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