Symplectic and Poisson geometry of the information geometry's Frobenius manifold

TL;DR

This paper establishes that the Frobenius manifold in information geometry possesses symplectic and Poisson structures, creating a link between different geometric theories.

Contribution

It demonstrates that the information geometry's Frobenius manifold is symplectic with Poisson structures, connecting Vinberg, Souriau, and Koszul theories with Frobenius manifolds.

Findings

Frobenius manifold is symplectic

Existence of Poisson structures on the manifold

Bridging of geometric theories

Abstract

We prove that the information geometry's Frobenius manifold is a symplectic manifold having Poisson structures. By proving this statement, a bridge is created between the theories developed by Vinberg, Souriau and Koszul and the Frobenius manifold approach. Until now these approaches seemed disconnected.