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＜電子ブック＞
An Introduction to Riemann-Finsler Geometry / by D. Bao, S.-S. Chern, Z. Shen
(Graduate Texts in Mathematics. ISSN:21975612 ; 200)

版	1st ed. 2000.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	2000
本文言語	英語
大きさ	XX, 435 p : online resource
冊子体	An introduction to Riemann-Finsler geometry / D. Bao, S.-S. Chern, Z. Shen ; : hbk
著者標目	*Bao, D author Chern, S.-S author Shen, Z author SpringerLink (Online service)
件　名	LCSH:Geometry FREE:Geometry
一般注記	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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4612-1268-3

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