Generalized conjugate connections and equiaffine structures on semi-Riemannian manifolds

Abstract

The generalized conjugate connections on semi-Riemannian manifolds are studied in this paper. A fact that an affine connection is equiaffine iff it's conjugate connection is equiaffine on statistical manifolds was generalized to the case of generalized conjugate connections on semi-Riemannian manifolds in [3]. The facts that the conjugate symmetry and conjugate Ricci-symmetry of statistical manifolds are sufficient conditions for α-connections to be equiaffine for any α(∈R) are generalized to the case of generalized conjugate connections on semi-Riemannian manifolds in this paper.