5 papers
On Duality, Legendre Bundles and Deformations
N. C. Combe, P. G. Combe, H. K. Nencka
We introduce the Legendre bundle, a geometric structure encoding the essential duality of dually flat (Hessian) manifolds, and demonstrate that both exponential families in informa…
Exploring information geometry: Recent Advances and Connections to Topological Field Theory
Noémie C. Combe, Philippe G. Combe, Hanna K. Nencka
This introductory text arises from a lecture given in Göteborg, Sweden, given by the first author and is intended for undergraduate students, as well as for any mathematically incl…
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…
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…
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…