Knots in Riemannian manifolds
| Autor: | Fang, Fuquan, Mendonca, S. |
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| Rok vydání: | 2008 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper we study submanifold with nonpositive extrinsic curvature in a positively curved manifold. Among other things we prove that, if $K\subset (S^n, g)$ is a totally geodesic submanifold in a Riemannian sphere with positive sectional curvature where $n\ge 5$, then $K$ is homeomorphic to $S^{n-2}$ and the fundamental group of the knot complement $\pi_1(S^n-K)\cong \Bbb Z$. Comment: 9 pages |
| Databáze: | arXiv |
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