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Please use this identifier to cite or link to this item: http://repositorio.ufba.br/ri/handle/ri/14030

Title: Hypersurfaces of ${\mathbb s}^{n+1}$ with two distinct principal curvatures
Other Titles: Glasgow Mathematical Journal
Authors: Barbosa, José Nelson Bastos
Issue Date: 2005
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 $S^{n-1}(r) \times S^1(\sqrt{1-r^2})$.
Description: p. 149-153
URI: http://repositorio.ufba.br/ri/handle/ri/14030
ISSN: 0017-0895
Appears in Collections:Artigos Publicados em Periódicos (IM)

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