A remark on almost umbilical hypersurfaces

Julien Roth

Address: Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, F-77454, Marne-la-Vallée, France

E-mail: julien.roth@univ-mlv.fr

Abstract: In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.

AMSclassification: primary 53A07; secondary 53A10, 53C20, 53C24.

Keywords: hypersurfaces, rigidity, pinching, Ricci curvature, umbilicity tensor, higher order mean curvatures, \theta -quasi-isometry.

DOI: 10.5817/AM2013-1-1