Anais da Academia Brasileira de Ciências | |
Hypersurfaces with constant mean curvature and two principal curvatures in n+1 | |
Luis J. Alías2  Sebastião C. De Almeida1  Aldir Brasil Jr.1  | |
[1] ,Universidad de Murcia Departamento de Matemáticas Espinardo Murcia ,Spain | |
关键词: Hypersurfaces; constant mean curvature; Simons formula; H(r)-torus; Hipersuperfícies; curvatura média constante; Fórmula de Simons; H(r)-toros; | |
DOI : 10.1590/S0001-37652004000300003 | |
来源: SciELO | |
【 摘 要 】
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.
【 授权许可】
CC BY
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