caa a22 4500 445836466 CHVBK 20180317145331.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00209-009-0627-3 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0627-3 Knots in Riemannian manifolds [Elektronische Daten] [Fuquan Fang, Sérgio Mendonça] 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 $${\pi _1(S^n-K)\cong \mathbb{Z}}$$. Springer-Verlag, 2009 Fundamental group nationallicence Positive curvature nationallicence Extrinsic curvature nationallicence Totally geodesic nationallicence Fang Fuquan Institute of Mathematics and Interdisciplinary Science, Capital Normal University, 100048, Beijing, People's Republic of China aut Mendonça Sérgio Departamento de Análise, Instituto de Matemática, Universidade Federal Fluminense, CEP 24020-140, Niterói, RJ, Brazil aut Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 425-431 0025-5874 267:1-2<425 2011 267 209 https://doi.org/10.1007/s00209-009-0627-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0627-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fang Fuquan Institute of Mathematics and Interdisciplinary Science, Capital Normal University, 100048, Beijing, People's Republic of China aut NATIONALLICENCE 700 1- Mendonça Sérgio Departamento de Análise, Instituto de Matemática, Universidade Federal Fluminense, CEP 24020-140, Niterói, RJ, Brazil aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 425-431 0025-5874 267:1-2<425 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer