非奇异Hermite矩阵流形上的Jacobi场

Jacobi Fields on the Manifold of Nonsingular Hermite Matrices

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.

In this paper, the manifold geometric structures of nonsingular Hermite matrices H（n） are considered. First, we define α- 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.