Knots in Riemannian manifolds |
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| Authors: | Fuquan Fang Sérgio Mendonça |
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| Institution: | 1. Institute of Mathematics and Interdisciplinary Science, Capital Normal University, 100048, Beijing, People’s Republic of China
2. Departamento de Análise, Instituto de Matemática, Universidade Federal Fluminense, Niterói, RJ, CEP 24020-140, Brazil
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| Abstract: | In this paper we study submanifolds 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 of codimension 2 in a Riemannian sphere with positive sectional curvature where n ≥ 5, then K is homeomorphic to S n–2 and the fundamental group of the knot complement ${\pi _1(S^n-K)\cong \mathbb{Z}}$ . |
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