Author | Bao, D. author |
---|---|
Title | An Introduction to Riemann-Finsler Geometry [electronic resource] / by D. Bao, S.-S. Chern, Z. Shen |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1268-3 |
Descript | XX, 435 p. online resource |
One Finsler Manifolds and Their Curvature -- 1 Finsler Manifolds and the Fundamentals of Minkowski Norms -- 2 The Chern Connection -- 3 Curvature and Schurโs Lemma -- 4 Finsler Surfaces and a Generalized GaussโBonnet 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 Syngeโs Theorem -- 9 The Cartan-Hadamard Theorem and Rauchโs First Theorem -- Three Special Finsler Spaces over the Reals -- 10 Berwald Spaces and Szabรณโs Theorem for Berwald Surfaces -- 11 Randers Spaces and an Elegant Theorem -- 12 Constant Flag Curvature Spaces and Akbar-Zadehโs Theorem -- 13 Riemannian Manifolds and Two of Hopfโs Theorems -- 14 Minkowski Spaces, the Theorems of Deicke and Brickell