Schroeder, Viktor (2000). Bounded geodesics in manifolds of negative curvature. Mathematische Zeitschrift, 235(4):817-828.
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics |
| Language: | English |
| Date: | 2000 |
| Deposited On: | 29 Nov 2010 16:27 |
| Last Modified: | 30 Nov 2022 14:23 |
| Publisher: | Springer |
| ISSN: | 0025-5874 |
| OA Status: | Closed |
| Publisher DOI: | https://doi.org/10.1007/s002090000166 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=1801585 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0990.53038 |
Schroeder, Viktor