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arXiv · 1801.07996

Topological rigidity for closed hypersurfaces of elliptic space forms

Eduardo Longa·Jaime Ripoll
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Abstract

We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absolute value of the principal curvatures, the hypersurface is diffeomorphic to a sphere or to a quotient of a sphere by a group action. We also prove another topological rigidity result for hypersurfaces of the sphere that involves the spherical image of its usual Gauss map.

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Eduardo Longa, Jaime Ripoll. 2018-01-24. Topological rigidity for closed hypersurfaces of elliptic space forms. https://arxiv.org/abs/1801.07996

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