| 非奇异Hermite矩阵流形上的Jacobi场 |
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| 引用本文： | 段晓敏,孙华飞. 非奇异Hermite矩阵流形上的Jacobi场[J]. 北京理工大学学报, 2011, 31(11): 1375-1378 |
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| 作者姓名： | 段晓敏 孙华飞 |
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| 作者单位： | 北京理工大学数学学院,北京,100081 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 讨论了非奇异Hermite矩阵流形H(n)的几何结构.定义其上的黎曼度量,给出了流形H(n)上的α-对偶联络和α-曲率张量.从微分几何的角度,研究流形H(n)上的Jacobi场,进而考虑测地线的收敛性,并举例说明结果.
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| 关 键 词： | Hermite矩阵 微分几何 Jacobi场 |
| 收稿时间： | 2010-12-20 |
Jacobi Fields on the Manifold of Nonsingular Hermite Matrices |
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| DUAN Xiao-min and SUN Hua-fei. Jacobi Fields on the Manifold of Nonsingular Hermite Matrices[J]. Journal of Beijing Institute of Technology(Natural Science Edition), 2011, 31(11): 1375-1378 |
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| Authors: | DUAN Xiao-min and SUN Hua-fei |
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| Affiliation: | School of Mathematics, Beijing Institute of Technology, Beijing 100081, China;School of Mathematics, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | In this paper,the manifold geometric structures of nonsingular Hermite matrices H(n) are considered.First,we define a Riemannian metric and introduce the dual α-connections and the α-curvature tensors.Then,the Jacobi fields on manifold H(n) have been considered to investigate the instability of the geodesics in view of differential geometry.Moreover,some examples are given to illustrate our results. |
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| Keywords: | Hermite matrices differential geometry Jacobi field |
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