Almost product structures on statistical manifolds and para-Kähler-like statistical submersions

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-Kähler-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.

17 pages; minor corrections; to appear in "Bulletin des Sciences Mathématiques"