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Bounded geodesics in manifolds of negative curvature


Schroeder, V (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 and dimension . Given a unit vector and a point 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.

Abstract

Let M be a complete Riemannian manifold with sectional curvature and dimension . Given a unit vector and a point 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.

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7 citations in Web of Science®
7 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2000
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:26
Publisher:Springer
ISSN:0025-5874
Publisher DOI:https://doi.org/10.1007/s002090000189
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1801585
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0990.53038

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