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On deformation of Poisson manifolds of hydrodynamic type

Luca Degiovanni·Franco Magri·Vincenzo Sciacca
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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.

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Luca Degiovanni, Franco Magri, Vincenzo Sciacca. 2001-03-27. On deformation of Poisson manifolds of hydrodynamic type. https://doi.org/10.1007/s00220-004-1190-8

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