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We studied sufficient conditions for generalized conjugate connections to be equiaffine on semi-Riemannian manifolds.
It is known that an affine connection is equiaffine if its conjugate connection is so on a statistical manifold. On the other hand, although an affine connection is equiaffine, its generalized conjugate connection may not be equiaffine on semi-Riemannian manifolds.
It is also known that a flatness, constancy of curvature, conjugate symmetry and conjugate Ricci-symmetry of a statistical manifold are sufficient conditions for a statistical manifold to have equiaffine structures.
We generalized the above results to semi-Riemannian manifolds to give sufficient conditions for generalized conjugate connections to be equiaffine and to study an equiaffinity of a family of generalized conjugate connections on semi-Riemannian manifolds.
The obtained result was published in an article entitled "Generalized conjugate connections and equiaffine structures on semi-Riemannian manifolds" (https://doi.org/ 10.1016/j.difgeo.2021.101829) to the SCI journal "Differential Geometry and its Applications".