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

We study Lagrangian and orthogonal splittings\textbf{\ }of quadratic vector spaces establishing an equivalence with complex product structures. Then we show that a Manin triple equipped generalized metric $\mathcal{G}+% \mathcal{B}$ such $\mathcal{B}$ is $\mathcal{O}$-operator extension $\mathcal{G}$ of mass -1 can be turned in another admits also splitting in\textbf{\ }Lie ideals. Conversely, ...