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

Research Article

School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

College 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.

Abstract

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 . 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.





Autor: Limei Cao, Didong Li, Erchuan Zhang, Zhenning Zhang, and Huafei Sun

Fuente: https://www.hindawi.com/



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