Topological rigidity for closed hypersurfaces of elliptic space forms
Differential Geometry
2018-09-28 v2
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.
Keywords
Cite
@article{arxiv.1801.07996,
title = {Topological rigidity for closed hypersurfaces of elliptic space forms},
author = {Eduardo Longa and Jaime Ripoll},
journal= {arXiv preprint arXiv:1801.07996},
year = {2018}
}
Comments
10 pages