Geodesic Flows in Manifolds of Nonpositive Curvature

I. Introduction-a quick historical survey of geodesic flows on negatively curved spaces. II. Preliminaries on Riemannian manifolds A. Riemannian metric and Riemannian volume element B. Levi Civita connection and covariant differentiation along curves C. Parallel translation of vectors along curves D. Curvature E. Geodesics and geodesic flow F. Riemannian exponential map and Jacobi vector fields G. Isometries and local isometries H. Geometry of the tangent bundle with the Sasaki metric III. Manifolds of nonpositive sectional curvature A. Definition of nonpositive curvature by triangle comparisons B. Growth of Jacobi vector fields C. The Riemannian exponential map is a covering map. Theorem of Cartan-Hadamard. D. Examples : Riemannian symmetric spaces E. Convexity properties and the Cartan Fixed Point Theorem F. Fundamental group of a nonpositively curved manifold. G. Rank of a nonpositively curved manifold IV. Sphere at infinity of a simply connected manifold of nonpositive sectional curvature A. Asymptotic geodesics and cone topology for M ~ (∞)