局部对称空间中常平均曲率超曲面的拼挤定理
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摘要
主要研究局部对称黎曼空间中具有常平均曲率的完备超曲面的拼挤问题.运用关于超曲面的全脐张量的Okumura型不等式及Omori-Yau极值原理,得到了一个关于超曲面的第二基本形式模长平方的拼挤定理.
In this paper,the complete hypersurfaces with constant mean curvature in locally symmetricspace have been discussed.By Okumura-type inequality of total umbilicity tensor and Omori-Yau maximum principle,apinching theorem for the squared length of the second fundamental form has been obtained.
In this paper,the complete hypersurfaces with constant mean curvature in locally symmetricspace have been discussed.By Okumura-type inequality of total umbilicity tensor and Omori-Yau maximum principle,apinching theorem for the squared length of the second fundamental form has been obtained.
引文
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[9]张士诚,吴报强.局部对称黎曼流形中具有常中曲率完备超曲面[J].数学物理学报(A辑),2010,30(4):1000-1005.
[10]MELNDEZ J.Rigidity Theorems for Hypersurfaces with Constant Mean Curvature[J].Bull Braz Math Soc(N.S.),2014,45(3):385-404.
[11]张剑锋,洪涛清.局部对称流形中具有常平均曲率的完备超曲面[J].纯粹数学与应用数学,2013,29(2):118-124.
[12]OMORI H.Isometric Immersions of Riemannian Manifolds[J].J Math Soc Japan,1967,19(2):205-214.
[13]YAU S T.Harmonic Functions on Complete Riemannian Manifolds[J].Comm Pure and Appl Math,2010,28(2):201-228.
[14]蔡开仁.欧氏空间中闭子流形的拓扑[J].数学年刊(A辑),1987,8(2):234-241.
[2]LI H Z.A Characterization of Clifford Minimal Hypersurfaces in S4[J].Proc Amer Math Soc,1995,123(10):3183-3187.
[3]CHENG Q M,ISHIKAWA S.A Characterization of the Clifford Torus[J].Proc Amer Math Soc,1999,127(3):819-828.
[4]ALENCAR H,CARMO M.Hypersurfaces with Constant Mean Curvature in Spheres[J].Proc Amer Math Soc,1994,120(4):1223-1229.
[5]何盼盼,姚纯青.球面上具有平行平均曲率向量的子流形[J].西南大学学报(自然科学版),2015,37(6):72-75.
[6]胡有婧,王伟,杨莉.de Sitter空间中的紧致类空子流形[J].西南师范大学学报(自然科学版),2015,40(2):33-36.
[7]水乃翔,吴国强.局部对称黎曼流形中的极小超曲面[J].数学年刊(A辑),1995,16(6):687-691.
[8]舒世昌,刘三阳.局部对称流形的具常平均曲率的完备超曲面[J].数学年刊(A辑),2004,25(1):99-104.
[9]张士诚,吴报强.局部对称黎曼流形中具有常中曲率完备超曲面[J].数学物理学报(A辑),2010,30(4):1000-1005.
[10]MELNDEZ J.Rigidity Theorems for Hypersurfaces with Constant Mean Curvature[J].Bull Braz Math Soc(N.S.),2014,45(3):385-404.
[11]张剑锋,洪涛清.局部对称流形中具有常平均曲率的完备超曲面[J].纯粹数学与应用数学,2013,29(2):118-124.
[12]OMORI H.Isometric Immersions of Riemannian Manifolds[J].J Math Soc Japan,1967,19(2):205-214.
[13]YAU S T.Harmonic Functions on Complete Riemannian Manifolds[J].Comm Pure and Appl Math,2010,28(2):201-228.
[14]蔡开仁.欧氏空间中闭子流形的拓扑[J].数学年刊(A辑),1987,8(2):234-241.