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arXiv · 1010.2863

A characterization of the extrinsic spheres in a Riemannian manifold

Ognian Kassabov
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Abstract

The following Theorem is proved: Let M be an n-dimensional (n>2) submanifold of a Riemannian manifold N. Suppose that through each point p of M there exist two (n-1)-dimensional extrinsic spheres of N, which are contained in M in a neighbourhood of p and are tangent to each other at p. Then M is totally geodesic in N or an extrinsic sphere of N.

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Ognian Kassabov. 2010-10-14. A characterization of the extrinsic spheres in a Riemannian manifold. https://arxiv.org/abs/1010.2863

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