On deformation of Poisson manifolds of hydrodynamic type
Exactly Solvable and Integrable Systems
2007-05-23 v1
Abstract
We study a class of deformations of infinite-dimensional Poisson manifolds of hydrodynamic type which are of interest in the theory of Frobenius manifolds. We prove two results. First, we show that the second cohomology group of these manifolds, in the Poisson-Lichnerowicz cohomology, is ``essentially'' trivial. Then, we prove a conjecture of B. Dubrovin about the triviality of homogeneous formal deformations of the above manifolds.
Keywords
Cite
@article{arxiv.nlin/0103052,
title = {On deformation of Poisson manifolds of hydrodynamic type},
author = {Luca Degiovanni and Franco Magri and Vincenzo Sciacca},
journal= {arXiv preprint arXiv:nlin/0103052},
year = {2007}
}
Comments
LaTeX file, 24 pages