Mathematics > Differential Geometry
[Submitted on 22 Jan 2014 (v1), last revised 28 Apr 2014 (this version, v2)]
Title:Riemannian Holonomy Groups of Statistical Manifolds
View PDFAbstract: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.
Submission history
From: Lin Jiu [view email][v1] Wed, 22 Jan 2014 15:43:27 UTC (13 KB)
[v2] Mon, 28 Apr 2014 14:17:32 UTC (14 KB)
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