# Bounded geodesics in manifolds of negative curvature

Schroeder, Viktor (2000). Bounded geodesics in manifolds of negative curvature. Mathematische Zeitschrift, 235(4):817-828.

## Abstract

Let M be a complete Riemannian manifold with sectional curvature ≤−1 and dimension ≥3. Given a unit vector v∈T$^1$M and a point x∈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 ≥3.

## Abstract

Let M be a complete Riemannian manifold with sectional curvature ≤−1 and dimension ≥3. Given a unit vector v∈T$^1$M and a point x∈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 ≥3.

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