Hypersurfaces with constant mean curvature and two principal curvatures in Sn+1
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| Format: | Artículo científico |
| Langue: | en |
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Academia Brasileira de Ciências
2004
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| _version_ | 1876486535973437440 |
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| author | Sebastião C. de Almeida |
| author_facet | Sebastião C. de Almeida |
| contents | Hypersurfaces with constant mean curvature and two principal curvatures in Sn+1 Sebastião C. de Almeida Luis J. Alías Aldir Brasil Multidisciplinaria (Ciencias Naturales y Exactas) H(r) torus Hypersurfaces Simons formula constant mean curvature 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. 2004 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32776303 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.3 Vol.76 |
| format | Artículo científico |
| id | redalyc_32776303 |
| institution | Redalyc |
| language | en |
| publishDate | 2004 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | Hypersurfaces with constant mean curvature and two principal curvatures in Sn+1 Sebastião C. de Almeida Multidisciplinaria (Ciencias Naturales y Exactas) H(r) torus Hypersurfaces Simons formula constant mean curvature Hypersurfaces with constant mean curvature and two principal curvatures in Sn+1 Sebastião C. de Almeida Luis J. Alías Aldir Brasil Multidisciplinaria (Ciencias Naturales y Exactas) H(r) torus Hypersurfaces Simons formula constant mean curvature 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. 2004 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32776303 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.3 Vol.76 |
| title | Hypersurfaces with constant mean curvature and two principal curvatures in Sn+1 |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) H(r) torus Hypersurfaces Simons formula constant mean curvature |
| url | https://www.redalyc.org/articulo.oa?id=32776303 |