HYPERSURFACES IN SPACE FORMS WITH SCALAR CURVATURE CONDITIONS
Let f : M^n→S^n+1真包含于R^n+2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n+1)-dimensional unit sphere S^n+1. Denote by S^n+1 the upper closed hemisphere. If f(M^n)包含于S+^n+1, then under some curvature conditions the authors can get that the isometric immersion is...
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| Published in | Acta mathematica scientia Vol. 24; no. 1; pp. 39 - 44 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
2004
Department of Mathematics, Central China Normal University, Wuhan,430079, China%Department of Mathematics, University of Science and Technology of China, Hefei,230026, China |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 |
| DOI | 10.1016/S0252-9602(17)30357-0 |
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| Abstract | Let f : M^n→S^n+1真包含于R^n+2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n+1)-dimensional unit sphere S^n+1. Denote by S^n+1 the upper closed hemisphere. If f(M^n)包含于S+^n+1, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature. |
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| AbstractList | Let f: Mn → Sn+1(∩) Rn+2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n+1)-dimensional unit sphere Sn+1. Denote by Sn+1+ the upper closed hemisphere. If f(Mn)(∩-) Sn+1+, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature. Let f:(Mn)→Sn+1⊂Rn+2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n + 1)-dimensional unit sphere Sn+1. Denote by the upper closed hemisphere. If f:(Mn)⊆S+n+1, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature. Let f : M^n→S^n+1真包含于R^n+2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n+1)-dimensional unit sphere S^n+1. Denote by S^n+1 the upper closed hemisphere. If f(M^n)包含于S+^n+1, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong on hypersurface of space form with costant scalar curvature. |
| Author | 徐森林 张运涛 |
| AuthorAffiliation | DepartmentofMathematics,CentralChinaNormalUniversity,Wuhan430079,China DepartmentofMathematics,UniversityofScienceandTechnologyofChina,Hefei230026,China |
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| Cites_doi | 10.1002/cpa.3160280303 10.1007/BF01444243 10.1007/BF01214381 10.1090/S0002-9939-1992-1093601-7 10.1007/BF01425237 |
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| Keywords | 53C42 Hypersurface 53A10 space form scalar curvature |
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| References | Cheng, Yau (bib4) 1975; 29 Leung (bib3) 1992; 114 Cheng (bib5) 1975; 143 Cheng, Yau (bib1) 1977; 225 Li (bib2) 1996; 305 Cheng (10.1016/S0252-9602(17)30357-0_bib4) 1975; 29 Leung (10.1016/S0252-9602(17)30357-0_bib3) 1992; 114 Li (10.1016/S0252-9602(17)30357-0_bib2) 1996; 305 Cheng (10.1016/S0252-9602(17)30357-0_bib5) 1975; 143 Cheng (10.1016/S0252-9602(17)30357-0_bib1) 1977; 225 |
| References_xml | – volume: 114 start-page: 1051 year: 1992 end-page: 1061 ident: bib3 article-title: An estimate of Ricci curvature for submanifolds and its application publication-title: Proc of the Amer Math Soc – volume: 143 start-page: 289 year: 1975 end-page: 293 ident: bib5 article-title: Eigenvalues comparison theorems and its applications publication-title: Math Z – volume: 305 start-page: 665 year: 1996 end-page: 672 ident: bib2 article-title: Hypersurfaces with constant scalar curvature in space forms publication-title: Math Ann – volume: 225 start-page: 195 year: 1977 end-page: 204 ident: bib1 article-title: Hypersurfaces with constant scalar curvature publication-title: Math Ann – volume: 29 start-page: 333 year: 1975 end-page: 354 ident: bib4 article-title: Differential equations on Riemannian manifold and their geometric applications publication-title: Comm Pure Appl Math – volume: 29 start-page: 333 year: 1975 ident: 10.1016/S0252-9602(17)30357-0_bib4 article-title: Differential equations on Riemannian manifold and their geometric applications publication-title: Comm Pure Appl Math doi: 10.1002/cpa.3160280303 – volume: 305 start-page: 665 year: 1996 ident: 10.1016/S0252-9602(17)30357-0_bib2 article-title: Hypersurfaces with constant scalar curvature in space forms publication-title: Math Ann doi: 10.1007/BF01444243 – volume: 143 start-page: 289 year: 1975 ident: 10.1016/S0252-9602(17)30357-0_bib5 article-title: Eigenvalues comparison theorems and its applications publication-title: Math Z doi: 10.1007/BF01214381 – volume: 114 start-page: 1051 year: 1992 ident: 10.1016/S0252-9602(17)30357-0_bib3 article-title: An estimate of Ricci curvature for submanifolds and its application publication-title: Proc of the Amer Math Soc doi: 10.1090/S0002-9939-1992-1093601-7 – volume: 225 start-page: 195 year: 1977 ident: 10.1016/S0252-9602(17)30357-0_bib1 article-title: Hypersurfaces with constant scalar curvature publication-title: Math Ann doi: 10.1007/BF01425237 |
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| Snippet | Let f : M^n→S^n+1真包含于R^n+2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n+1)-dimensional unit sphere S^n+1. Denote... Let f:(Mn)→Sn+1⊂Rn+2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n + 1)-dimensional unit sphere Sn+1. Denote by the... Let f: Mn → Sn+1(∩) Rn+2 be an n-dimensional complete oriented Riemannian manifold minimally immersed in an (n+1)-dimensional unit sphere Sn+1. Denote by Sn+1+... |
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| Title | HYPERSURFACES IN SPACE FORMS WITH SCALAR CURVATURE CONDITIONS |
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