Constancy of curvature and conformal-projective flatness of statistical manifolds

TL;DR

This paper investigates the relationship between the constancy of curvature and conformal-projective flatness in statistical manifolds, focusing on the properties of the conformal-projective curvature tensor.

Contribution

It establishes new connections between curvature constancy and flatness conditions in statistical manifolds, expanding understanding of their geometric structure.

Findings

Identifies conditions linking curvature constancy to flatness.

Provides new identities for conformal-projective curvature tensor.

Discusses implications for the geometry of statistical manifolds.

Abstract

An identity of conformal-projective curvature tensor of a statistical manifold is studied in this paper. The relation between the constancy of curvature and conformal-projective flatness of statistical manifolds is also discussed.