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2000 Hooke's law in statistical manifolds and divergences
Masayuki Henmi, Ryoichi Kobayashi
Nagoya Math. J. 159: 1-24 (2000).


The concept of the canonical divergence is defined for dually flat statistical manifolds in terms of the Legendre transform between dual affine coordinates. In this article, we introduce a new two point function defined for any triple $(g, \nabla, \nabla^{*})$ of a Riemannian metric $g$ and two affine connections $\nabla$ and $\nabla^{*}$. We show that this interprets the canonical divergence without refering to the existence of special coordinates (dual affine coordinates) but in terms of only classical mechanics concerning $\nabla$- and $\nabla^{*}$-geodesics. We also discuss the properties of the two point function and show that this shares some important properties with the canonical divergence defined on dually flat statistical manifolds.


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Masayuki Henmi. Ryoichi Kobayashi. "Hooke's law in statistical manifolds and divergences." Nagoya Math. J. 159 1 - 24, 2000.


Published: 2000
First available in Project Euclid: 27 April 2005

zbMATH: 0991.53007
MathSciNet: MR1783561

Primary: 53B99
Secondary: 62F99

Rights: Copyright © 2000 Editorial Board, Nagoya Mathematical Journal

Vol.159 • 2000
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