| Reduction of Volume—preserving Flows on an n—dimensional Manifold |
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| 引用本文： | Yong-aiZheng De-binHuang Zeng-rongLiu. Reduction of Volume—preserving Flows on an n—dimensional Manifold[J]. 应用数学学报(英文版), 2003, 19(1): 129-134. DOI: 10.1007/s10255-003-0089-z |
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| 作者姓名： | Yong-aiZheng De-binHuang Zeng-rongLiu |
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| 作者单位： | [1]DepartmentofMathematics,YangzhouUniversity,YangzhouUniversity,Yangzhou225006,China [2]DepartmentofMathematics,ShanghaiUniversity,ShanGHAI200436,China |
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| 摘 要： | A geometric reduction procedure for volume-preserving flows with a volume-preserving symme-try on an n-dimensional manifold is obtained.Instead of the coordinate-dependent theory and the concrete coordinate transformation,we xhow that a volume-preserving flow with a one-parameter volume-preserving symmetry on an n-dimensional manifold can be reduced to a volume-preserving flow on the corresponding (n-1)-dimensional quotient space.More generally,if it admits an r-parameter volume-preserving commutable symmetry,then the reduced folw preserves the corresponding (n-r)-dimensional volume form.
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| 关 键 词： | 体积保存流 流形 约化 李群 体积保存对称 广义微分形式 |
Reduction of Volume-preserving Flows on an n-dimensional Manifold |
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| Yong-ai Zheng,De-bin Huang,Zeng-rong Liu. Reduction of Volume-preserving Flows on an n-dimensional Manifold[J]. Acta Mathematicae Applicatae Sinica, 2003, 19(1): 129-134. DOI: 10.1007/s10255-003-0089-z |
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| Authors: | Yong-ai Zheng De-bin Huang Zeng-rong Liu |
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| Affiliation: | (1) Department of Mathematics, Yangzhou University, Yangzhou 225006, China (E-mail: zhengyongai@163.com), CN;(2) Department of Mathematics, Shanghai University, Shanghai 200436, China, CN |
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| Abstract: | A geometric reduction procedure for volume-preserving flows with a volume-preserving symmetry on an n-dimensional manifold is obtained. Instead of the coordinate-dependent theory and the concrete coordinate transformation, we show that a volume-preserving flow with a one-parameter volume-preserving symmetry on an n-dimensional manifold can be reduced to a volume-preserving flow on the corresponding (n-1)-dimensional quotient space. More generally, if it admits an r-parameter volume-preserving commutable symmetry, then the reduced flow preserves the corresponding (n- r)-dimensional volume form. |
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| Keywords: | Reduction volume-preserving flow manifold Lie group volume-preserving symmetry |
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