关于局部对称共形平坦空间中具有常数量曲率的子流形

Abstract

Abstract:

In this paper, the authors discuss the submanifolds with constant scalar curvature in a locally symmetric and conformally flat space, and obtain some intrinsic rigidity theorems.

Key words: Locally symmetric, Conformally flat, Scalar curvature, Submanifold, Umbilical

CLC Number:

53C42

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SONG Wei-Dong, LIU Min. On Submanifolds with Constant Scalar Curvature in a Locally Symmetric and Conformally Flat Space[J].Acta mathematica scientia,Series A, 2010, 30(4): 1102-1110.

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References

[1] Cheng S Y, Yau S T. Hypersurfaces with constant scalar curvature. Math Ann, 1977, 225: 195--204

[2] Zhang J F. A rigidity theorem for submanifolds in Sⁿ^+p with constant scatav curvature. Zhejiang Univ Sci, 2005, 6A(4): 322--328

[3] Shu S C, Liu S Y. Complete submanifolds with constant scalar curvature in the hyperbolic space. Advances in Math, 2006, 35(2): 154--166

[4] Yau S T. Submanifolds with constant mean curvature I-!I. Amer J Math, 1974, 96: 346--366; 1975, 97: 76--100

[5] Li A M, Li J M. An intrinsic rigidity theorem for minimal submanifolds in sphere. Arch Math, 1992, 58: 582--594

[6] Chern S S, do Carmo M, Kobayashi S. Minimal submanifolds of a sphere with second fundamental form of canstant length. Funcational Analysis and Related Fields, 1975: 59--75

[7] 宋卫东. 关于具有平行第二基本形式的伪脐子流形. 数学物理学报, 2000, 20(2): 158--162

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On Submanifolds with Constant Scalar Curvature in a Locally Symmetric and Conformally Flat Space

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