Lifts of left invariant statistical structures

Articles in Press

Document Type : Original Article

Authors

1 Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran

2 Faculty of Sciences, University of Zabol, Zabol, Iran

Abstract

This paper investigates two interconnected themes in statistical geometry: the lifting of statistical structures from a Lie group to its tangent Lie group and the study of locally product-like statistical manifolds. We first explore the geometric and algebraic properties of lifting statistical structures, focusing on the compatibility conditions and invariance properties that allow such structures to be naturally extended to the tangent Lie group. Key results include the construction of lifted connections, the behavior of statistical curvature tensors, and the preservation of conjugate symmetry under the lifting process. In the second part, we study locally product-like statistical manifolds, which generalize the notion of product manifolds in the context of statistical geometry. We characterize these manifolds by their decomposition into orthogonal statistical submanifolds and analyze their curvature properties, conjugate symmetry, and compatibility with statistical connections. Explicit examples are provided to illustrate both the lifting process and the structure of locally product-like statistical manifolds. These findings deepen the understanding of statistical geometry in the context of Lie groups, tangent bundles, and product-like structures, offering new insights into their geometric and algebraic properties.

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AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 20 January 2026

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