On the geodesic flow of surfaces of nonpositive curvature
Abstract
Let $S$ be a surface of nonpositive curvature of genus bigger than 1 (i.e. not the torus). We prove that any flat strip in the surface is in fact a flat cylinder. Moreover we prove that the number of homotopy classes of such flat cylinders is bounded.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- January 2003
- DOI:
- 10.48550/arXiv.math/0301010
- arXiv:
- arXiv:math/0301010
- Bibcode:
- 2003math......1010R
- Keywords:
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- Dynamical Systems