体积元保持变换下的一类特殊预给定数量曲率问题

Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (5): 1317-1322.

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On a Special Class of Prescribed Scalar Curvature Problems with Volume Element Preserving Deformations

QIU Liang-Hua

Qianjiang College, Hangzhou Normal University, Hangzhou 310012

Received:2009-12-25 Revised:2011-03-10 Online:2011-10-25 Published:2011-10-25
Supported by:
浙江省教育厅基金(Y200906404)资助

In this paper, the author discusses a special class of prescribed scalar curvature problems with volume element preserving deformations by the help of variational method. It is obtained that when the prescribed scalar curvature only depends on one of the two product manifolds and some extra condtions are satisfied, the volume element preserving deformation exists.

Key words: Volume element preserving deformation, Variational methods

CLC Number:

35J20

Cite this article

QIU Liang-Hua. On a Special Class of Prescribed Scalar Curvature Problems with Volume Element Preserving Deformations[J].Acta mathematica scientia,Series A, 2011, 31(5): 1317-1322.

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[4] 丘成桐, 孙理察. 微分几何讲义. 北京: 高等教育出版社, 2004

[5] 王志张. 体积元保持变换下预给定数量曲率的度量存在性. 数学年刊, 2008, 29A(6): 829--850

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