Mathematische Zeitschrift

, Volume 235, Issue 4, pp 817–828

Bounded geodesics in manifolds of negative curvature

  • Viktor Schroeder
Original article


Let M be a complete Riemannian manifold with sectional curvature \(\leq -1\) and dimension \(\geq 3\). Given a unit vector \(v\in T^1M\) and a point \(x\in M\) we prove the existence of a complete geodesic through x whose tangent vector never comes close to v. As a consequence we show the existence of a bounded geodesic through every point in a complete negatively pinched manifold with finite volume and dimension \(\geq 3\).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Viktor Schroeder
    • 1
  1. 1.Institut für Mathematik, Universität Zürich, Winterthurer Strasse 190, CH-8057 Zürich, Switzerland (e-mail:

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