| 紧致黎曼流形的TORSE-FORMING向量场 |
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| 引用本文： | 张学山. 紧致黎曼流形的TORSE-FORMING向量场[J]. 东北大学学报(自然科学版), 1985, 0(3) |
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| 作者姓名： | 张学山 |
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| 作者单位： | 西安冶金建筑学院数学教研室 |
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| 摘 要： | 本文讨论紧致黎曼流形中的Torse-forming向量场,得到此向量场同流形的Ricci曲率之间的关系,运用Torse-forming向量场的性质给出了容有这种向量场的紧致无边流形同球面共形的一个条件,并讨论了Torse-forming向量场诱导到一般子流形的情况。
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| 关 键 词： | 黎曼流形 紧致黎曼流形 向量场 子流形 |
The Torse-Forming Vector Fields in a Compact Riemannian Manifold |
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| Zhang Xueshan. The Torse-Forming Vector Fields in a Compact Riemannian Manifold[J]. Journal of Northeastern University(Natural Science), 1985, 0(3) |
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| Authors: | Zhang Xueshan |
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| Affiliation: | Zhang Xueshan |
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| Abstract: | Analyzes the torse-forming vector fields in a compact Riemannian manifold and then finds out the relationship between torse-forming vector fields and Ricci curvature of Riemannian manifold. Utilizing the properties of torse-forming vector field, a condition that compact Riemannian manifold admitting this vector field is conformal to a sphere in the Euclidean space is obtained. Discusses further the torss-forming vector field in case that it ia induced to the sub-manifold of Riemannian manifold. |
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| Keywords: | Riemannian manifold compact Riemannian manifold torse-forming vector field submanifold. |
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