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.

中文翻译：

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统计流形上的几乎乘积结构和类 Kähler 类统计淹没

目前工作的主要目的是研究具有几乎产品结构的统计流形。我们证明了在 Kurose 的意义上的常曲率的类 para-Kähler 统计流形的统计结构是 Hessian 结构。我们还推导出与几乎产品结构兼容的统计淹没的主要属性。几个重要的例子说明了结果。