Hypersurfaces with constant mean curvature and two principal curvatures in <img id="_x0000_i1025" src="../../../../img/revistas/aabc/v76n3/a03img01.gif" align=absbottom>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 fundam...
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| Format: | Article |
| Language: | English |
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Academia Brasileira de Ciências
2004-09-01
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| Series: | Anais da Academia Brasileira de Ciências |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652004000300003&tlng=en |
| _version_ | 1798015485081550848 |
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| author | Luis J. Alías Sebastião C. de Almeida Aldir Brasil Jr. |
| author_facet | Luis J. Alías Sebastião C. de Almeida Aldir Brasil Jr. |
| author_sort | Luis J. Alías |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T15:35:16Z |
| format | Article |
| id | doaj.art-07c472f0f1fb41cab0be041e76149c76 |
| institution | Directory Open Access Journal |
| issn | 1678-2690 |
| language | English |
| last_indexed | 2024-04-11T15:35:16Z |
| publishDate | 2004-09-01 |
| publisher | Academia Brasileira de Ciências |
| record_format | Article |
| series | Anais da Academia Brasileira de Ciências |
| spelling | doaj.art-07c472f0f1fb41cab0be041e76149c762022-12-22T04:15:58ZengAcademia Brasileira de CiênciasAnais da Academia Brasileira de Ciências1678-26902004-09-0176348949710.1590/S0001-37652004000300003Hypersurfaces with constant mean curvature and two principal curvatures in <img id="_x0000_i1025" src="../../../../img/revistas/aabc/v76n3/a03img01.gif" align=absbottom>n+1Luis J. Alías0Sebastião C. de Almeida1Aldir Brasil Jr.2Universidad de MurciaUniversidade Federal do CearáUniversidade Federal do CearáIn 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.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652004000300003&tlng=enHypersurfacesconstant mean curvatureSimons formulaH(r)-torus |
| spellingShingle | Luis J. Alías Sebastião C. de Almeida Aldir Brasil Jr. Hypersurfaces with constant mean curvature and two principal curvatures in <img id="_x0000_i1025" src="../../../../img/revistas/aabc/v76n3/a03img01.gif" align=absbottom>n+1 Anais da Academia Brasileira de Ciências Hypersurfaces constant mean curvature Simons formula H(r)-torus |
| title | Hypersurfaces with constant mean curvature and two principal curvatures in <img id="_x0000_i1025" src="../../../../img/revistas/aabc/v76n3/a03img01.gif" align=absbottom>n+1 |
| title_full | Hypersurfaces with constant mean curvature and two principal curvatures in <img id="_x0000_i1025" src="../../../../img/revistas/aabc/v76n3/a03img01.gif" align=absbottom>n+1 |
| title_fullStr | Hypersurfaces with constant mean curvature and two principal curvatures in <img id="_x0000_i1025" src="../../../../img/revistas/aabc/v76n3/a03img01.gif" align=absbottom>n+1 |
| title_full_unstemmed | Hypersurfaces with constant mean curvature and two principal curvatures in <img id="_x0000_i1025" src="../../../../img/revistas/aabc/v76n3/a03img01.gif" align=absbottom>n+1 |
| title_short | Hypersurfaces with constant mean curvature and two principal curvatures in <img id="_x0000_i1025" src="../../../../img/revistas/aabc/v76n3/a03img01.gif" align=absbottom>n+1 |
| title_sort | hypersurfaces with constant mean curvature and two principal curvatures in img id x0000 i1025 src img revistas aabc v76n3 a03img01 gif align absbottom n 1 |
| topic | Hypersurfaces constant mean curvature Simons formula H(r)-torus |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652004000300003&tlng=en |
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