| 局部对称共形平坦黎曼流形中的极小子流形 |
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| 引用本文： | 孙华飞.局部对称共形平坦黎曼流形中的极小子流形[J].东北大学学报(自然科学版),1991(3). |
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| 作者姓名： | 孙华飞 |
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| 作者单位： | 东北工学院数学系 |
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| 摘 要： | 本文把陈省身等的结论推广到了环绕空间是局部对称共形平坦的情形,即获得:设M~n是局部对称共形平坦黎曼流形N~(n+p)中的紧致极小子流形。如果 则M~n是全测地的或。其中S是M~n第二基本形式长度平方,K为N~(n+p)的数量曲率,T_c,t_c分别是N~(n+P)的R_(icei)曲率的上,下确界。
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| 关 键 词： | 黎曼流形 极小子流形 局部对称 共形平坦 全测地 |
Minimal Submanifolds in a Locally Symmetric and Conformal Flat Riemannian Manifold |
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| Sun Huafei.Minimal Submanifolds in a Locally Symmetric and Conformal Flat Riemannian Manifold[J].Journal of Northeastern University(Natural Science),1991(3). |
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| Authors: | Sun Huafei |
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| Abstract: | A conclusion by S. S. Chern et al is generalized and extended to the case that the surrounding space is locally symmetric and conformal flat. Let Mn be a compact minimal submanifold in a locally symmetric and conformal flat Rie-mannian manifold Nn+p and ifthen Mn is either totally geodesic orwhere S is the square of the length of the second fundamental form of Mn , K the scalar curvature of Nn+p , Tc and tc the definite upper and lower bounds of Ricci's curvature of Nn+p, respectively. |
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| Keywords: | Riemann manifold minimal submanifold local symmetry con-formal flat totally geodesic |
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