On deformation of Poisson manifolds of hydrodynamic type

Degiovanni, Luca; Magri, Franco; Sciacca, Vincenzo

On deformation of Poisson manifolds of hydrodynamic type

Authors

Degiovanni, Luca

Magri, Franco

Sciacca, Vincenzo

Description

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.
LaTeX file, 24 pages