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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We introduce a quarter-symmetric projective conformal non-metric connection family and study its geometrical properties. Further we investigate the geometries of a symmetric-type quarter-symmetric projective conformal non-metric connection satisfying the Schur?s theorem.

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