Extrinsic radius pinching for hypersurfaces of space forms

Julien Roth (1)

1 IECN - Institut Élie Cartan de Nancy

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.

Mots clés: Extrinsic radius; pinching; hypersurfaces; space forms

Domaines: Géométrie différentielle [math.DG]

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