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On the Gauss map of hypersurfaces with constant scalar curvature in spheres |
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| Authors: | Hilá rio Alencar Harold Rosenberg Walcy Santos |
| Institution: | Departamento de Matemática, Universidade Federal de Alagoas, 57072-900, Maceió, AL, Brazil ; Institut de Mathématiques de Jussieu, 2 Place Jussieu, 75251 Paris, France ; Departamento de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil |
| Abstract: | In this work we consider connected, complete and orientable hypersurfaces of the sphere  with constant nonnegative  -mean curvature. We prove that under subsidiary conditions, if the Gauss image of  is contained in a closed hemisphere, then  is totally umbilic. |
| Keywords: | $r$-mean curvature spheres Gauss image |
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