Extrinsic radius pinching for hypersurfaces of space forms

Abstract : 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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Submitted on : Monday, March 20, 2006 - 2:16:10 PM
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Julien Roth. Extrinsic radius pinching for hypersurfaces of space forms. Differential Geometry and its Applications, Elsevier, 2007, 25 (5), pp.485-499. ⟨hal-00021278⟩

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