Rigidity theorems of Clifford Torus

Anais da Academia Brasileira de Ciências

Luiz A. M. Sousa Jr.¹ 

[1] ,Universidade Federal do Rio de Janeiro Instituto de Matemática Rio de Janeiro RJ ,Brazil

关键词: minimal hypersurfaces;    scalar curvature;    principal curvatures;    Clifford Torus;    Hipersuperfícies mínimas;    curvatura escalar;    curvaturas principais;    toro de Clifford;   

DOI  :  10.1590/S0001-37652001000300003

来源: SciELO

【 摘 要 】

Let M be an n-dimensional closed minimally immersed hypersurface in the unit sphere Sn + 1. Assume in addition that M has constant scalar curvature or constant Gauss-Kronecker curvature. In this note we announce that if M has (n - 1) principal curvatures with the same sign everywhere, then M is isometric to a Clifford Torus .

【 授权许可】

CC BY   
 All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License