Hypersurfaces with constant mean curvature and two principal curvatures in n+1
In this paper we consider compact oriented hypersurfaces M with constant mean curvature and two principal curvatures immersed in the Euclidean sphere. In the minimal case, Perdomo (Perdomo 2004) andWang (Wang 2003) obtained an integral inequality involving the square of the norm of the second fundamental form of M, where equality holds only if M is the Clifford torus. In this paper, using the traceless second fundamental form of M, we extend the above integral formula to hypersurfaces with constant mean curvature and give a new characterization of the H(r)-torus.
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Academia Brasileira de Ciências
2004
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oai:scielo:S0001-376520040003000032004-08-20Hypersurfaces with constant mean curvature and two principal curvatures in n+1Alías,Luis J.Almeida,Sebastião C. deBrasil Jr.,Aldir Hypersurfaces constant mean curvature Simons formula H(r)-torus In this paper we consider compact oriented hypersurfaces M with constant mean curvature and two principal curvatures immersed in the Euclidean sphere. In the minimal case, Perdomo (Perdomo 2004) andWang (Wang 2003) obtained an integral inequality involving the square of the norm of the second fundamental form of M, where equality holds only if M is the Clifford torus. In this paper, using the traceless second fundamental form of M, we extend the above integral formula to hypersurfaces with constant mean curvature and give a new characterization of the H(r)-torus.info:eu-repo/semantics/openAccessAcademia Brasileira de CiênciasAnais da Academia Brasileira de Ciências v.76 n.3 20042004-09-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652004000300003en10.1590/S0001-37652004000300003 |
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English |
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| author |
Alías,Luis J. Almeida,Sebastião C. de Brasil Jr.,Aldir |
| spellingShingle |
Alías,Luis J. Almeida,Sebastião C. de Brasil Jr.,Aldir Hypersurfaces with constant mean curvature and two principal curvatures in n+1 |
| author_facet |
Alías,Luis J. Almeida,Sebastião C. de Brasil Jr.,Aldir |
| author_sort |
Alías,Luis J. |
| title |
Hypersurfaces with constant mean curvature and two principal curvatures in n+1 |
| title_short |
Hypersurfaces with constant mean curvature and two principal curvatures in n+1 |
| title_full |
Hypersurfaces with constant mean curvature and two principal curvatures in n+1 |
| title_fullStr |
Hypersurfaces with constant mean curvature and two principal curvatures in n+1 |
| title_full_unstemmed |
Hypersurfaces with constant mean curvature and two principal curvatures in n+1 |
| title_sort |
hypersurfaces with constant mean curvature and two principal curvatures in n+1 |
| description |
In this paper we consider compact oriented hypersurfaces M with constant mean curvature and two principal curvatures immersed in the Euclidean sphere. In the minimal case, Perdomo (Perdomo 2004) andWang (Wang 2003) obtained an integral inequality involving the square of the norm of the second fundamental form of M, where equality holds only if M is the Clifford torus. In this paper, using the traceless second fundamental form of M, we extend the above integral formula to hypersurfaces with constant mean curvature and give a new characterization of the H(r)-torus. |
| publisher |
Academia Brasileira de Ciências |
| publishDate |
2004 |
| url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652004000300003 |
| work_keys_str_mv |
AT aliasluisj hypersurfaceswithconstantmeancurvatureandtwoprincipalcurvaturesinn1 AT almeidasebastiaocde hypersurfaceswithconstantmeancurvatureandtwoprincipalcurvaturesinn1 AT brasiljraldir hypersurfaceswithconstantmeancurvatureandtwoprincipalcurvaturesinn1 |
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