Fuquan Fang, S. Mendonca
Published 2008-01-15, updated 2008-08-25Version 2
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 $\pi_1(S^n-K)\cong \Bbb Z$.
Examples of Riemannian manifolds with positive curvature almost everywhere
Kähler manifolds and fundamental groups of negatively $δ$-pinched manifolds
Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds
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