# Almost product structures on statistical manifolds and para-K\"ahler-like statistical submersions

## TL;DR

This paper explores statistical manifolds with almost product structures, showing that para-K"ahler-like manifolds of constant curvature are Hessian and analyzing compatible statistical submersions with illustrative examples.

## Contribution

It establishes that para-K"ahler-like statistical manifolds of constant curvature are Hessian and studies properties of compatible statistical submersions.

## Key findings

- Para-K"ahler-like statistical manifolds of constant curvature are Hessian.
- Properties of statistical submersions compatible with almost product structures are derived.
- Several nontrivial examples illustrate the theoretical results.

## Abstract

The main purpose of the present work is to investigate statistical manifolds endowed with almost product structures. We prove that the statistical structure of a para-K\"{a}hler-like statistical manifold of constant curvature in the Kurose's sense is a Hessian structure. We also derive the main properties of statistical submersions which are compatible with almost product structures. The results are illustrated by several nontrivial examples.