Equiaffine structure and conjugate Ricci-symmetry of a statistical manifold

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 [4] and [5]. 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 a weaker condition than conjugate symmetry. A condition for conjugate symmetry and conjugate Ricci-symmetry to coincide is also given.