Jacobi fields on the manifold of Gamma exponential

Abstract

In this paper, the Gamma exponential distribution is treated as a statistical manifold and the geometric structures of Gamma exponential manifold are considered. First, we de- fine a Riemannian metric and introduce the a - connections and the a - curvature tensor. Then, the Jacobi field on the Gamma exponential manifold has been considered to investigate the instability of the geodesics in view of differential geometry. Moreover, some examples are given to illustrate our results.

Keywords:

• Gamma exponential manifold
• a - connection
• a - curvature tensor
• Jacobi field

Subject Classification:

• 53B20
• 22E60
• 47A64