Work

Infinitesimal Affine Transformations and Mutual Curvatures on Statistical Manifolds and Their Tangent Bundles

Year: 2023

Type: article

Abstract: The purpose of this paper is to find some conditions under which the tangent bundle TM has a dualistic structure. Then, we introduce infinitesimal affine transformations on statistical manifolds and investigate these structures on a special statistical distribution and the tangent bundle of a statistical manifold too. Moreover, we also study the mutual curvatures of a statistical manifold M and its tangent bundle TM and we investigate their relations. More precisely, we obtain the mutual curvatures of well-known connections on the tangent bundle TM (the complete, horizontal, and Sasaki connections) and we study the vanishing of them.

Source: Axioms

DOI: 10.3390/axioms12070667

Authors: Esmaeil Peyghan, Davood Seifipour, Ion Mihai

Institutions: Arak University, Islamic Azad University, Abadan, University of Bucharest

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,779

OpenAlex ID: W4383552228

FWCI: 1.032

Cites: 14

Cited by: 3

Related to: 10