Hypersurfaces with constant mean curvature and two principal curvatures in n+1

Anais da Academia Brasileira de Ciências

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】

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