Gradient solitons on statistical manifolds

Abstract

We provide necessary and sufficient conditions for some particular couples (g, ∇) of pseudo-Riemannian metric and affine connections to be statistical structures if we have gradient almost Einstein, almost Ricci, almost Yamabe solitons, or a more general type of solitons in the manifold. In particular cases, we establish a formula for the volume of the manifold and give a lower and an upper bound for the norm of the Ricci curvature tensor field.