An Introduction to Riemann-Finsler Geometry
Published on 6. December 2012
XX, 435 pages
978-1-4612-1268-3 (ISBN)
Description
PRELIMINARY TEXT. DO NOT USE. Finsler geometry is a metric generalization of Riemannian geometry and has become a comparatively young branch of differential geometry. Although Finsler geometry has its genesis in Riemann's 1854 "Habilitationsvortrag," its systematic study was not initiated until 1918 by Finsler, and the fundamentals were not completely formulated until the mid-thirties. Later, however, the field underwent a rapid development by mathematicians and physicists of many countries. The main purpose of this book is to study the metric geometry of Finsler manifolds. Portions of the book generalize some standard concepts from Riemannian geometry to the Finsler setting, while other
Reviews / Votes
"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
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D. Bao | S.-S. Chern | Z. Shen
An Introduction to Riemann-Finsler Geometry
Book
10/2012
Springer
€69.54
Shipment within 15-20 days
Content
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.
