Almost product structures on statistical manifolds and para-K\"ahler-like statistical submersions
Differential Geometry
2021-08-10 v2
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.
Keywords
Cite
@article{arxiv.1904.09411,
title = {Almost product structures on statistical manifolds and para-K\"ahler-like statistical submersions},
author = {Gabriel-Eduard Vîlcu},
journal= {arXiv preprint arXiv:1904.09411},
year = {2021}
}
Comments
17 pages; minor corrections; to appear in "Bulletin des Sciences Math\'ematiques"