An Introduction to Riemann-Finsler Geometry

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.