Statistical Biharmonicity of Identity Maps

TL;DR

This paper explores the statistical biharmonicity of identity maps between statistical and Riemannian statistical manifolds, deriving a new class of manifolds satisfying semi-equiaffine conditions and characterizing their structures.

Contribution

It introduces a novel class of statistical manifolds based on biharmonicity and characterizes their structures in the context of constant curvature spaces.

Findings

Derived a new class of statistical manifolds satisfying semi-equiaffine conditions.

Established the statistical structures for manifolds of constant curvature.

Linked the tension field of identity maps to the Tchevychev vector field.

Abstract

The tension field of the identity map from a statistical manifold to a Riemannian statistical manifold, which shares the same Riemannian metric, is the Tchevychev vector field multiplied by negative one. We derive a new class of statistical manifolds that satisfy the semi-equiaffine condition based on the statistical biharmonicity of the identity map. Furthermore, we determine the statistical structures of this class, when the pair of the manifold and the Riemannian metric is a simply connected complete Riemannian manifold of constant curvature.