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arXiv · 1302.3167

Equiaffine Structure and Conjugate Ricci-symmetry of a Statistical Manifold

Chol-Rim Min·Won-Hak Ri·Hyong-Chol O
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Abstract

A condition for a statistical manifold to have an equiaffine structure is studied. The facts that dual flatness and conjugate symmetry of a statistical manifold are sufficient conditions for a statistical manifold to have an equiaffine structure were obtained in [2] and [3]. In this paper, a fact that a statistical manifold, which is conjugate Ricci-symmetric, has an equiaffine structure is given, where conjugate Ricci-symmetry is weaker condition than conjugate symmetry. A condition for conjugate symmetry and conjugate Ricci-symmetry to coincide is also given.

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Chol-Rim Min, Won-Hak Ri, Hyong-Chol O. 2013-02-13. Equiaffine Structure and Conjugate Ricci-symmetry of a Statistical Manifold. https://arxiv.org/abs/1302.3167

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