Bounded geodesics in manifolds of negative curvature
by
Viktor Schroeder
University of Zurich

Let M be a complete Riemannian manifold with sectional curvature < -1 and dimension > 2. Given a unit tangent vector v of M and a point x in M we prove the existence of a complete geodesic through x whose tangent vectors never come close to v. With the same methods we show the existence of a bounded geodesic through every point in a complete negatively pinched manifold with finite volume and dimension > 2. The dimesion assumption is essential for the proof and the corresponding results are open for surfaces.

Date received: February 18, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caca-46.