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 con- jecture of B. Dubrovin about the triviality of homogeneous formal deformations of the above manifolds.
L DEGIOVANNI, F MAGRI, SCIACCA V (2005). On deformation of Poisson manifolds of Hydrodynamic type. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 253(1), 1-24 [10.1007/s00220-004-1190-8].
On deformation of Poisson manifolds of Hydrodynamic type
SCIACCA, Vincenzo
2005-01-01
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 con- jecture of B. Dubrovin about the triviality of homogeneous formal deformations of the above manifolds.
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