3 papers
math.AG2022
Symplectic and Poisson geometry of the information geometry's Frobenius manifold
Noemie Combe, Philippe Combe, Hanna Nencka
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…
math.AG2021
Algebraic properties of the information geometry's fourth Frobenius manifold
N. C. Combe, P. G. Combe, H. K. Nencka
Recently, it has been shown that the statistical manifold, related to exponential families, has a Frobenius manifold structure and appears as the fourth class of Frobenius manifold…
math.AG2021
Pseudo-elliptic geometry of a class of Frobenius-manifolds & Maurer--Cartan structures
N. Combe, Ph. Combe, H. Nencka
The recently discovered fourth class of Frobenius manifolds by Combe--Manin in opened and highlighted new geometric domains to explore. The guiding mantra of this article is to sho…