Compatibility of Gauss maps with metrics
classification
🧮 math.DG
math.AP
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gaussbrieflycasecompatibilityconditionsdiscussgeneralgive
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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
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