Article Dans Une Revue Differential Geometry and its Applications Année : 2007

Extrinsic radius pinching for hypersurfaces of space forms

Julien Roth

Résumé

We prove some pinching results for the extrinsic radius of compact hypersurfaces in space forms. We show that if the pinching condition 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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hal-00021278 , version 1 (20-03-2006)

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  • HAL Id : hal-00021278 , version 1

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Julien Roth. Extrinsic radius pinching for hypersurfaces of space forms. Differential Geometry and its Applications, 2007, 25 (5), pp.485-499. ⟨hal-00021278⟩
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