Statistical Lie algebras of a constant curvature and locally conformally K\"ahler Lie algebras

TL;DR

This paper explores the geometric structures of statistical manifolds with constant non-zero curvature, demonstrating their realization as Hessian level sets and constructing related Sasakian and locally conformally Kähler Lie algebras.

Contribution

It introduces a novel connection between statistical manifolds of constant curvature and the construction of Sasakian and l.c.K Lie algebras.

Findings

Statistical manifolds of constant non-zero curvature can be realized as Hessian level sets.

A Sasakian structure can be constructed on the tangent bundle times real line.

A new class of locally conformally Kähler Lie algebras is derived from statistical Lie algebras.

Abstract

We show that a statistical manifold manifold of a constant non-zero curvature can be realised as a level line of Hessian potential on a Hessian cone. We construct a Sasakian structure on $TM\times\R$ by a statistical manifold manifold of a constant non-zero curvature on $M$. By a statistical Lie algebra of a constant non-zero Lie algebra we construct a l.c.K Lie algebra.