| 具有特殊交换性质的共形Jacobi算子的黎曼流形 |
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| 引用本文： | 张磊,赵艳.具有特殊交换性质的共形Jacobi算子的黎曼流形[J].河南师范大学学报(自然科学版),2012,40(2):34-36. |
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| 作者姓名： | 张磊 赵艳 |
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| 作者单位： | 1. 河南工业大学理学院,郑州,450006
2. 河南省轻工业学校基础教学部,郑州,450006 |
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| 摘 要： | 设(M,g)是维数为m的黎曼流形,m>3.共形Jacobi算子JW(X)定义为:JW(X):Y→W(Y,X)X;对于任意的p∈M以及任意的X,Y∈TpM,当g(X,Y)=0时,都有等式JW(X)JW(Y)=JW(Y)JW(X)成立的特殊交换性质的共形Jacobi算子的黎曼流形进行了分类.
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| 关 键 词： | 共形 Jacobi算子 局部共形平坦的黎曼流形 |
Manifolds With Special Commuting Conformal Jacobi Operators |
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| ZHANG Lei
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ZHAO Yan.Manifolds With Special Commuting Conformal Jacobi Operators[J].Journal of Henan Normal University(Natural Science),2012,40(2):34-36. |
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| Authors: | ZHANG Lei ZHAO Yan |
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| Institution: | 1.College of Science,Henan University of Technology,Zhengzhou 450006,China; 2.Department of Basic,The School of Henan Light Industry,Zhengzhou 450001,China) |
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| Abstract: | Let(M,g) be a Riemannian manifold of dimension m>3.The conformal Jacobi operator JW(X) is defined by JW(X)Y=W(Y,X)X.If for all p∈M and for each pair of orthogonal vectors X,Y∈TpM,the equality JW(X)JW(Y)=JW(Y)JW(X) holds.Conformal flat Riemannian manifolds are classified in terms of special commutation properties of their conformal Jacobi operators. |
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| Keywords: | conformal Jacobi operator locally conformally flat Riemannian manifold |
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