HYPERSURFACES WITH CONSTANT MEAN-CURVATURE IN SPHERES

Authors
ALENCAR H DOCARMO M
Citation
H. Alencar et M. Docarmo, HYPERSURFACES WITH CONSTANT MEAN-CURVATURE IN SPHERES, Proceedings of the American Mathematical Society, 120(4), 1994, pp. 1223-1229
Citations number
10
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
120
Issue
4
Year of publication
1994
Pages
1223 - 1229
Database
ISI
SICI code
0002-9939(1994)120:4<1223:HWCMIS>2.0.ZU;2-Z
Abstract
Let M(n) be a compact hypersurface of a sphere with constant mean curv ature H. We introduce a tensor phi, related to H and to the second fun damental form, and show that if \phi\2 < B(H), where B(H) not-equal 0 is a number depending only on H and n, then either 10(12) = 0 or \phi\ 2 = B(H). We also characterize all M(n) with \phi\2 = B(H).