A new result about almost umbilical hypersurfaces of real space forms

J. Roth


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.




Almost-umbilical hypersurfaces; space forms; constant scalar curvature

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Bulletin of the Aust. Math. Soc., copyright Australian Mathematical Publishing Association Inc.