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https://repositorio.ufba.br/handle/ri/14030
metadata.dc.type: | Artigo de Periódico |
Title: | Hypersurfaces of ${\mathbb s}^{n+1}$ with two distinct principal curvatures |
Other Titles: | Glasgow Mathematical Journal |
Authors: | Barbosa, José Nelson Bastos |
metadata.dc.creator: | Barbosa, José Nelson Bastos |
Abstract: | The aim of this paper is to prove that the Ricci curvature ${\rm Ric}_M$ of a complete hypersurface $M^n$, $n\,{\ge}\,3$, of the Euclidean sphere $\mathbb{S}^{n+1}$, with two distinct principal curvatures of multiplicity 1 and $n-1$, satisfies $\sup {\rm Ric}_M\,{\ge}\,\inf\, f(H)$, for a function\, $f$ depending only on $n$ and the mean curvature $H$. Supposing in addition that $M^n$ is compact, we will show that the equality occurs if and only if $H$ is constant and $M^n$ is isometric to a Clifford torus $S^{n-1}(r) \times S^1(\sqrt{1-r^2})$. |
metadata.dc.publisher.country: | Brasil |
metadata.dc.rights: | Acesso Aberto |
URI: | http://repositorio.ufba.br/ri/handle/ri/14030 |
Issue Date: | 2005 |
Appears in Collections: | Artigo Publicado em Periódico (IME) |
Files in This Item:
File | Description | Size | Format | |
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JOSÉ N. BARBOSA.pdf | 71,5 kB | Adobe PDF | View/Open |
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