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VOL. 57 | 2010 Statistical manifolds and affine differential geometry
Hiroshi Matsuzoe

Editor(s) Motoko Kotani, Masanori Hino, Takashi Kumagai

Abstract

In this paper, we give a summary of geometry of statistical manifolds, and discuss relations between information geometry and affine differential geometry. Dually flat spaces and canonical divergence functions are important objects in information geometry. We show that such objects can be generalized in the framework of affine differential geometry.

In addition, we give a brief summary of geometry of statistical manifolds admitting torsion, which is regarded as a quantum version of statistical manifolds. We discuss relations between statistical manifolds admitting torsion and geometry of affine distributions.

Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1201.53011
MathSciNet: MR2648267

Digital Object Identifier: 10.2969/aspm/05710303

Subjects:
Primary: 53A15, 53A30, 53B05, 62B10, 81Q70

Rights: Copyright © 2010 Mathematical Society of Japan

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