| 正定矩阵流形上的Jacobi场 |
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| 引用本文： | 罗志坤,孙华飞,李帝东.正定矩阵流形上的Jacobi场[J].北京理工大学学报,2013,33(6):657-660. |
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| 作者姓名： | 罗志坤 孙华飞 李帝东 |
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| 作者单位： | 北京理工大学数学学院,北京,100081;北京理工大学数学学院,北京,100081;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(61179031,10932002) |
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| 摘 要： | 讨论了正定矩阵流形D(n)的几何结构.新定义其上的黎曼度量,给出了流形 D(n)上的黎曼联络和黎曼曲率张量.从微分几何的角度,研究流形 D(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： | 正定矩阵 黎曼联络 黎曼曲率张量 Jacobi场 |
| 收稿时间： | 2012/9/18 0:00:00 |
Jacobi Fields on the Manifold of Positive Definite Matrices |
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| LUO Zhi-kun,SUN Hua-fei and LI Di-dong.Jacobi Fields on the Manifold of Positive Definite Matrices[J].Journal of Beijing Institute of Technology(Natural Science Edition),2013,33(6):657-660. |
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| Authors: | LUO Zhi-kun SUN Hua-fei and LI Di-dong |
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| Institution: | School of Mathematics, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | In this paper, the geometric structures of positive definite matrices D(n) are studied. First, we define a Riemannian metric and introduce the Riemannian connection and the Riemannian curvature tensor. Then, the Jacobi fields on manifold D(n) have been considered to investigate the instability of the geodesics in view of differential geometry. Moreover, one example is given to illustrate our result. |
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| Keywords: | positive definite matrices Riemannian connection Riemannian curvature tensor Jacobi field |
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