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

Noemie Combe, Philippe Combe, Hanna Nencka

Published 2022-01-19Version 1

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.