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arXiv · 0903.3225

Compatibility of Gauss maps with metrics

J. Eschenburg·B. S. Kruglikov·V. S. Matveev·R. Tribuzy
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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

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J. Eschenburg, B. S. Kruglikov, V. S. Matveev, R. Tribuzy. 2009-03-18. Compatibility of Gauss maps with metrics. https://doi.org/10.1016/j.difgeo.2009.10.004

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