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arXiv · 2201.07517

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

Noemie Combe·Philippe Combe·Hanna Nencka
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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.

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Noemie Combe, Philippe Combe, Hanna Nencka. 2022-01-19. Symplectic and Poisson geometry of the information geometry's Frobenius manifold. https://arxiv.org/abs/2201.07517

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