A characterization of the extrinsic spheres in a Riemannian manifold

Details A characterization of the extrinsic spheres in a Riemannian manifold A characterization of the extrinsic spheres in a Riemannian manifold

2010-10-14

arxiv.org/abs/1010.2863v1

Riv. Mat. Univ. Parma, 5 (1996),15-21

Mathematics

Differential Geometry

7 pages

Scientific paper

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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