Manifolds of negative curvature
Manifolds of negative curvature
IntroductionACm function/on a riemannian manifold M is convex provided its hessian (second covariant differential) is positive semidefinite, or equivalently if (/o <t)"5:0 for every geodesic a in M. We shall apply this notion in a variety of ways to the study of manifolds of negative or nonpositive curvature.Convexity has, of …