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

被引：22

作者：

Vilcu, Gabriel-Eduard ^{[1
,2
]}

机构：

[1] Univ Bucharest, Fac Math & Comp Sci, Res Ctr Geometry Topol & Algebra, Str Acad 14,Sect 1, Bucharest 70109, Romania

[2] Petr Gas Univ Ploiesti, Dept Cybernet Econ Informat Finance & Accountancy, Bd Bucuresti 39, Ploiesti 100680, Romania

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2021年 / 171卷

关键词：

Affine connection; Conjugate connection; Statistical manifold; Almost product structure; Statistical submersion; FUNDAMENTAL EQUATIONS; SUBMANIFOLDS; CONNECTIONS;

D O I：

10.1016/j.bulsci.2021.103018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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-Kahler-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. (C) 2021 Elsevier Masson SAS. All rights reserved.

引用

页数：21

共 47 条

[1] An affine submersion with horizontal distribution and its applications [J].