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Publication date: 22 June 2021

Khadidja Addad and Seddik Ouakkas

In this paper, we give some properties of the α-connections on statistical manifolds and we study the α-conformal equivalence where we develop an expression of curvature R…

Abstract

Purpose

In this paper, we give some properties of the α-connections on statistical manifolds and we study the α-conformal equivalence where we develop an expression of curvature R¯ for ¯ in relation to those for ∇ and ^.

Design/methodology/approach

In the first section of this paper, we prove some results about the α-connections of a statistical manifold where we give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds treated in [1, 3], and we construct some examples.

Findings

We give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds, we give the relations between curvature tensors and we construct some examples.

Originality/value

We give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds, we give the relations between curvature tensors and we construct some examples.

Details

Arab Journal of Mathematical Sciences, vol. 30 no. 1
Type: Research Article
ISSN: 1319-5166

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