On deformation of Poisson manifolds of hydrodynamic type

Details On deformation of Poisson manifolds of hydrodynamic type On deformation of Poisson manifolds of hydrodynamic type

2001-03-27

arxiv.org/abs/nlin/0103052v1

Comm. Math. Phys. 253 (2005), 1-24

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX file, 24 pages

Scientific paper

10.1007/s00220-004-1190-8

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.

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