Compatibility of Gauss maps with metrics

Abstract

We give necessary and sufficient conditions on a smooth local map of a Riemannian manifold $M^m$ into the sphere $S^m$ to be the Gauss map of an isometric immersion $u:M^m\to R^n$, $n=m+1$. We briefly discuss the case of general $n$ as well

14 pages, no figures

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