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Advances in Mathematical Physics
Volume 2014, Article ID 832683, 6 pages
Research Article

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

1School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
2School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
3College of Applied Sciences, Beijing University of Technology, Beijing 100124, China

Received 24 September 2014; Revised 15 December 2014; Accepted 15 December 2014; Published 30 December 2014

Academic Editor: Carlo Cattani

Copyright © 2014 Limei Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 . 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.