Rigidity theorems of Clifford Torus

Authors
Citation
Lam. Sousa, Rigidity theorems of Clifford Torus, AN AC BRASI, 73(3), 2001, pp. 327-332
Citations number
4
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Multidisciplinary
Journal title
ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS
ISSN journal
0001-3765 → ACNP
Volume
73
Issue
3
Year of publication
2001
Pages
327 - 332
Database
ISI
SICI code
0001-3765(200109)73:3<327:RTOCT>2.0.ZU;2-V
Abstract
Let M be an n-dimensional closed minimally immersed hypersurface in the uni t sphere Sn+1. Assume in addition that M has constant scalar curvature or c onstant Gauss-Kronecker curvature. In this note we announce that if M has ( n - 1) principal curvatures with the same sign everywhere, then M is isomet ric to a Clifford Torus S-1 (root1/n) x Sn-1 (rootn-1/n).