Sharp inequalities and solitons for statistical submersions

In this research article, initially, we prove some sharp inequalities on statistical submersions involving Ricci and scalar curvatures of the statistical manifolds. In addition, we establish the geometrical bearing on statistical submersions in terms of Ricci-Bourguignon soliton. Moreover, we characterize the fibers of a statistical submersion as Ricci-Bourguignon solitons with conformal vector field. Finally, in the particular case when the vertical potential vector field of the Ricci-Bourguignon soliton is of gradient type, we derive a Poisson equation for a statistical submersion.