A Statistical Cohomogeneity One Metric on the Upper Plane with Constant Negative Curvature

Abstract EN

we analyze the geometrical structures of statisticalmanifold S consisting of all the wrapped Cauchy distributions.

We prove that S is a simplyconnected manifold with constant negative curvature K=-2.

However, it is not isometric tothe hyperbolic space because S is noncomplete.

In fact, S is approved to be a cohomogeneityone manifold.

Finally, we use several tricks to get the geodesics and explore the divergenceperformance of them by investigating the Jacobi vector field.