Jacobi Fields on the Manifold of Positive Definite Matrices

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.