Hypersurfaces of ${\mathbb s}^{n+1}$ with two distinct principal curvatures
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2005 |
| Tipo de documento: | Artigo |
| Idioma: | eng |
| Título da fonte: | Repositório Institucional da UFBA |
| Texto Completo: | http://repositorio.ufba.br/ri/handle/ri/14030 |
Resumo: | p. 149-153 |
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Barbosa, José Nelson BastosBarbosa, José Nelson Bastos2013-12-02T10:55:54Z2013-12-02T10:55:54Z20050017-0895http://repositorio.ufba.br/ri/handle/ri/14030v. 47, n. 1p. 149-153The 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 $S^{n-1}(r) \times S^1(\sqrt{1-r^2})$.Submitted by Edileide Reis (leyde-landy@hotmail.com) on 2013-12-02T10:55:53Z No. of bitstreams: 1 JOSÉ N. BARBOSA.pdf: 73215 bytes, checksum: fc78972257bb84288de7f45ec645d1c5 (MD5)Made available in DSpace on 2013-12-02T10:55:54Z (GMT). No. of bitstreams: 1 JOSÉ N. BARBOSA.pdf: 73215 bytes, checksum: fc78972257bb84288de7f45ec645d1c5 (MD5) Previous issue date: 2005http://dx.doi.org.ez10.periodicos.capes.gov.br/10.1017/S0017089504002137reponame:Repositório Institucional da UFBAinstname:Universidade Federal da Bahia (UFBA)instacron:UFBAHypersurfaces of ${\mathbb s}^{n+1}$ with two distinct principal curvaturesGlasgow Mathematical Journalinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleBrasilinfo:eu-repo/semantics/openAccessengORIGINALJOSÉ N. BARBOSA.pdfJOSÉ N. BARBOSA.pdfapplication/pdf73215https://repositorio.ufba.br/bitstream/ri/14030/1/JOS%c3%89%20N.%20BARBOSA.pdffc78972257bb84288de7f45ec645d1c5MD51LICENSElicense.txtlicense.txttext/plain1345https://repositorio.ufba.br/bitstream/ri/14030/2/license.txtff6eaa8b858ea317fded99f125f5fcd0MD52TEXTJOSÉ N. BARBOSA.pdf.txtJOSÉ N. BARBOSA.pdf.txtExtracted texttext/plain11112https://repositorio.ufba.br/bitstream/ri/14030/3/JOS%c3%89%20N.%20BARBOSA.pdf.txt5b25ce9cd1b363ac60319a8d20962e69MD53ri/140302022-08-08 13:17:35.568oai:repositorio.ufba.br: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Repositório InstitucionalPUBhttp://192.188.11.11:8080/oai/requestopendoar:19322022-08-08T16:17:35Repositório Institucional da UFBA - Universidade Federal da Bahia (UFBA)false |
| dc.title.pt_BR.fl_str_mv |
Hypersurfaces of ${\mathbb s}^{n+1}$ with two distinct principal curvatures |
| dc.title.alternative.pt_BR.fl_str_mv |
Glasgow Mathematical Journal |
| title |
Hypersurfaces of ${\mathbb s}^{n+1}$ with two distinct principal curvatures |
| spellingShingle |
Hypersurfaces of ${\mathbb s}^{n+1}$ with two distinct principal curvatures Barbosa, José Nelson Bastos |
| title_short |
Hypersurfaces of ${\mathbb s}^{n+1}$ with two distinct principal curvatures |
| title_full |
Hypersurfaces of ${\mathbb s}^{n+1}$ with two distinct principal curvatures |
| title_fullStr |
Hypersurfaces of ${\mathbb s}^{n+1}$ with two distinct principal curvatures |
| title_full_unstemmed |
Hypersurfaces of ${\mathbb s}^{n+1}$ with two distinct principal curvatures |
| title_sort |
Hypersurfaces of ${\mathbb s}^{n+1}$ with two distinct principal curvatures |
| author |
Barbosa, José Nelson Bastos |
| author_facet |
Barbosa, José Nelson Bastos |
| author_role |
author |
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Barbosa, José Nelson Bastos Barbosa, José Nelson Bastos |
| description |
p. 149-153 |
| publishDate |
2005 |
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2005 |
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2013-12-02T10:55:54Z |
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2013-12-02T10:55:54Z |
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0017-0895 |
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v. 47, n. 1 |
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0017-0895 v. 47, n. 1 |
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