Abstract
Let N N be a complete simply connected Riemannian manifold of constant sectional curvature ≠ 0 \ne 0 . Let M M be an immersed Riemannian hypersurface of N N . The Gauss map on M M based at a point p p in N N is defined. Suppose a Gauss map on M M has constant rank less than the dimension of M M ; then M M is generated by Riemannian submanifolds with constant sectional curvature. The sectional curvature of each of these generating submanifolds of M M has the same sign as the sectional curvature of N N .
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