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metadata.dc.type: | Artigo de Periódico |
Title: | A Ricci inequality for hypersurfaces in the sphere |
Other Titles: | Archiv der Mathematik |
Authors: | Costa, Ézio de Araújo |
metadata.dc.creator: | Costa, Ézio de Araújo |
Abstract: | Let M n be a complete Riemannian manifold immersed isometrically in the unity Euclidean sphere Sn+1. In [9], B. Smyth proved that if M n , n ≧ 3, has sectional curvature K and Ricci curvature Ric, with inf K > −∞, then sup Ric ≧ (n − 2) unless the universal covering M~n of M n is homeomorphic to Rn or homeomorphic to an odd-dimensional sphere. In this paper, we improve the result of Smyth. Moreover, we obtain the classification of complete hypersurfaces of Sn+1. with nonnegative sectional curvature. |
metadata.dc.rights: | Acesso Aberto |
URI: | http://repositorio.ufba.br/ri/handle/ri/13623 |
Issue Date: | 2005 |
Appears in Collections: | Artigo Publicado em Periódico (IME) |
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