| 关于拟常曲率空间子流形的调和与Killing向量场 |
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| 引用本文： | 李建华. 关于拟常曲率空间子流形的调和与Killing向量场[J]. 东北大学学报(自然科学版), 1986, 0(3) |
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| 作者姓名： | 李建华 |
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| 作者单位： | 东北工学院数学系 |
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| 摘 要： | 本文研究了一般拟常曲率空间N的紧可定向子流形M上的调和向量场,射影Killing向量场以及保形Killing向量场。给出了M上任意向量场所满足的两个积分公式,并且运用这两个积分公式讨论了M上的调和向量场、射影Killing向量场,保形Killing向量场的平行性、不存在性与M的主曲率之间的关系。同时在N为一种特殊的拟常曲率空间即S—流形的假设下又得出了进一步的结论。本文中主要结果是Shetty,D.J.在常曲率空间子流形上类似结果的推广。
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| 关 键 词： | 拟常曲率空间 紧可定向子流形 调和向量场 Killing向量场 |
On the Harmonic and Killing Vector Fields in a Submanifold of Quasi-constant Curvature Space |
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| Li Jianhua. On the Harmonic and Killing Vector Fields in a Submanifold of Quasi-constant Curvature Space[J]. Journal of Northeastern University(Natural Science), 1986, 0(3) |
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| Authors: | Li Jianhua |
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| Abstract: | Two integral formulas, satisfied with any vector field on a compact orien-table submanifold M of general quasi-constant curvature space N, are given. With these integral formulas, the parallelism of harmonic, projective Killing and conformal Killing vector fields on M are examined, as well as the relationship between the nonexistence of these vector fields and the principal curvature of M under certain conditions. Thus the resulds given by D. J. Shetty are generalized. Some particular properties of N,ie. a S-manifold, are also obtained. |
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| Keywords: | quasi-constant curvature space compact orientable submanifold harmonic vector field killing vector field |
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