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A NEW RESULT ABOUT ALMOST UMBILICAL HYPERSURFACES OF REAL SPACE FORMS

Part of: Global differential geometry

Published online by Cambridge University Press:  14 October 2014

JULIEN ROTH
JULIEN ROTH*
Affiliation:
Laboratoire d’Analyse et de Mathématiques Appliquées, UPEM-UPEC, CNRS, F-77454 Marne-la-Vallée, France email julien.roth@u-pem.fr
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Abstract

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In this short note, we prove that an almost umbilical compact 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.

Keywords

almost umbilical hypersurfacesspace formsconstant scalar curvature

MSC classification

Secondary: 53C20: Global Riemannian geometry, including pinching 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 1 , February 2015 , pp. 145 - 154
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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