Gradient solitons on statistical manifolds

TL;DR

This paper characterizes when certain metric-connection pairs form statistical structures on manifolds with various soliton conditions, providing formulas and bounds related to the manifold's geometry.

Contribution

It offers necessary and sufficient conditions for statistical structures involving gradient solitons, along with formulas for volume and Ricci curvature bounds.

Findings

Derived conditions for statistical structures with gradient solitons.

Established volume formulas for the manifold.

Provided bounds for Ricci curvature tensor norm.

Abstract

We provide necessary and sufficient conditions for some particular couples $(g,\nabla)$ of pseudo-Riemannian metrics 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 on 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.