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体积元保持变换下的一类特殊预给定数量曲率问题

On a Special Class of Prescribed Scalar Curvature Problems with Volume Element Preserving Deformations
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摘要 该文利用变分方法对于紧致无边界Reimann流形M×N上的在一类特殊预给定数量曲率条件下的体积元保持变换的存在性进行研究.得到了下述结果:当预给定的数量曲率仅依赖于乘积流形中的一个,并且再满足某些其他条件的时候,体积元保持变换存在. 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.
作者 裘良华
机构地区 杭州师范大学钱江学院
出处 《数学物理学报（A辑）》 CSCD 北大核心 2011年第5期1317-1322,共6页 Acta Mathematica Scientia
基金 浙江省教育厅基金(Y200906404)资助
关键词 体积元保持变换 变分方法. Volume element preserving deformation Variational methods.
分类号 O175.29 [理学—基础数学]
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参考文献5

  • 1Gilbarg D, Trudinger N S. Elliptic Partial Differential Equations of Second Order. Berlin: Springer, 1983.
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  • 4王志张.体积元保持变换下预给定数量曲率的度量存在性[J].数学年刊（A辑）,2008,29(6):829-850. 被引量：1
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二级参考文献10

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数学物理学报（A辑）
2011年 第5期

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