On the Gauss map of hypersurfaces with constant scalar curvature in spheres

Alencar, Hilário; Rosenberg, Harold; Santos, Walcy

doi:10.1090/S0002-9939-04-07493-3

On the Gauss map of hypersurfaces with constant scalar curvature in spheres
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by Hilário Alencar, Harold Rosenberg and Walcy Santos

Proc. Amer. Math. Soc. 132 (2004), 3731-3739

DOI: https://doi.org/10.1090/S0002-9939-04-07493-3

Published electronically: July 12, 2004

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Abstract:

In this work we consider connected, complete and orientable hypersurfaces of the sphere $\mathbb {S}^{n+1}$ with constant nonnegative $r$-mean curvature. We prove that under subsidiary conditions, if the Gauss image of $M$ is contained in a closed hemisphere, then $M$ is totally umbilic.

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