Simple Closed Geodesics in Hyperbolic 3-Manifolds
几何拓扑
2007-05-23 v1 微分几何
摘要
This paper determines which orientable hyperbolic 3-manifolds contain simple closed geodesics. The Fuchsian group corresponding to the thrice-punctured sphere generates the only example of a complete non-elementary orientable hyperbolic 3-manifold that does not contain a simple closed geodesic. We do not assume that the manifold is geometrically finite or that it has finitely generated fundamental group.
引用
@article{arxiv.math/9801071,
title = {Simple Closed Geodesics in Hyperbolic 3-Manifolds},
author = {Colin Adams and Joel Hass and Peter Scott},
journal= {arXiv preprint arXiv:math/9801071},
year = {2007}
}
备注
7 pages, to appear in the Bulletin of the London Mathematical Society