Riemannian Holonomy Groups of Statistical Manifolds

Didong Li; Huafei Sun; Chen Tao; Lin Jiu

Riemannian Holonomy Groups of Statistical Manifolds

Differential Geometry 2014-04-29 v2

Authors: Didong Li , Huafei Sun , Chen Tao , Lin Jiu

Abstract

Normal distribution manifolds play essential roles in the theory of information geometry, so do holonomy groups in classification of Riemannian manifolds. After some necessary preliminaries on information geometry and holonomy groups, it is presented that the corresponding Riemannian holonomy group of the $d$ -dimensional normal distribution is $SO\left(\frac{d\left(d+3\right)}{2}\right)$ , for all $d\in\mathbb{N}$ . As a generalization on exponential family, a list of holonomy groups follows.

Keywords

statistical manifold Riemannian holonomy group normal distribution manifold information geometry exponential family SO(n)

Cite

@article{arxiv.1401.5706,
  title  = {Riemannian Holonomy Groups of Statistical Manifolds},
  author = {Didong Li and Huafei Sun and Chen Tao and Lin Jiu},
  journal= {arXiv preprint arXiv:1401.5706},
  year   = {2014}
}

Comments

11 pages

Riemannian Holonomy Groups of Statistical Manifolds

Abstract

Keywords

Cite

Comments

Related papers