A Statistical Cohomogeneity One Metric on the Upper Plane with Constant Negative Curvature - Limei Cao; Didong Li; Erchuan Zhang; Zhenning Zhang; Huafei Sun (Advances in Mathematical Physics)
we analyze the geometrical structures of statistical manifold S consisting of all the wrapped Cauchy distributions. We prove that S is a simply connected manifold with constant negative curvature K=-2. However, it is not isometric to the hyperbolic space because S is noncomplete. In fact, S is approved to be a cohomogeneity one manifold. Finally, we use several tricks to get the geodesics and explore the divergence performance of them by investigating the Jacobi vector field.