English

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"