A new result about almost umbilical hypersurfaces of real space forms

J. Roth

Abstract


In this short note, we prove that an almost umbilical hypersurface of a real space form with almost Codazzi umbilicity tensor is embedded, diffeomorphic and quasi-isometric to a round sphere. Then, we derive a new characterisation of geodesic spheres in space forms.

DOI:

10.1017/S0004972714000732

Keywords


Almost-umbilical hypersurfaces; space forms; constant scalar curvature



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