Extrinsic radius pinching for hypersurfaces of space forms
classification
🧮 math.DG
keywords
pinchingextrinsicformshypersurfacesradiusspacealmostcompact
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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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