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vol.73 issue3Tangency quantum cohomology and characteristic numbersErratum to "Bernstein-type theorems in hypersurfaces with constant mean curvature" [An Acad Bras Cienc 72(2000): 301-310] author indexsubject indexarticles search
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Anais da Academia Brasileira de Ciências

Print version ISSN 0001-3765On-line version ISSN 1678-2690

Abstract

SOUSA JR., LUIZ A. M.. Rigidity theorems of Clifford Torus. An. Acad. Bras. Ciênc. [online]. 2001, vol.73, n.3, pp.327-332. ISSN 0001-3765.  http://dx.doi.org/10.1590/S0001-37652001000300003.

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 03ab.gif (725 bytes).

Keywords : minimal hypersurfaces; scalar curvature; principal curvatures; Clifford Torus.

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