1302.3167 (Chol-Rim Min et al.)

Equiaffine Structure and Conjugate Ricci-symmetry of a Statistical
Manifold    [PDF]

Chol-Rim Min, Won-Hak Ri, Hyong-Chol O

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.

View original: http://arxiv.org/abs/1302.3167