Extrinsic radius pinching for hypersurfaces of space forms

Details Extrinsic radius pinching for hypersurfaces of space forms Extrinsic radius pinching for hypersurfaces of space forms

2006-03-21

arxiv.org/abs/math/0603494v1

Mathematics

Differential Geometry

20 pages, 1 figure

Scientific paper

We prove some pinching results for the extrinsic radius of compact
hypersurfaces in space forms. We show that if the pinching condion is strong
enough with a dependance on the norm of the second foundamental form, then the
hypersurface is diffeomorphic and almost isometric to a geodesic hypersphere.

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