  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.

Differential Geometry