Closed hypersurfaces of with constant mean curvature and zero Gauss-Kronecker curvature
We consider a closed hypersurface with identically zero Gauss-Kronecker curvature. We prove that if M3 has constant mean curvature H, then M3 is minimal, i.e., H=0. This result extends Ramanathan's classification (Math. Z. 205 (1990) 645-658) result of closed minimal hypersurfaces of with vanis...
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| Veröffentlicht in: | Comptes rendus. Mathématique 2005-03, Vol.340 (6), p.437-440 |
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| container_title | Comptes rendus. Mathématique |
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| creator | Lusala, Tsasa de Oliveira, Andre Gomes |
| description | We consider a closed hypersurface with identically zero Gauss-Kronecker curvature. We prove that if M3 has constant mean curvature H, then M3 is minimal, i.e., H=0. This result extends Ramanathan's classification (Math. Z. 205 (1990) 645-658) result of closed minimal hypersurfaces of with vanishing Gauss-Kronecker curvature. To cite this article: T. Lusala, A. Gomes de Oliveira, C. R. Acad. Sci. Paris, Ser. I 340 (2005). Resume Nous considerons une hypersurface fermee (compacte et sans bord) a courbure de Gauss-Kronecker identiquement nulle. Nous prouvons que si la courbure moyenne H de M3 est constante, alors l'hypersurface M3 est necessairement minimale, c.a.d, H=0. Ce resultat generalise celui obtenu dans l'article de Ramanathan (Math. Z. 205 (1990) 645-658) concernant les hypersurfaces fermees minimales a courbure de Gauss-Kronecker identiquement nulle dans. Pour citer cet article: T. Lusala, A. Gomes de Oliveira, C. R. Acad. Sci. Paris, Ser. I 340 (2005). |
| doi_str_mv | 10.1016/j.crma.2005.01.005 |
| format | Article |
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| ispartof | Comptes rendus. Mathématique, 2005-03, Vol.340 (6), p.437-440 |
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| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| title | Closed hypersurfaces of with constant mean curvature and zero Gauss-Kronecker curvature |
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