On deformation ofPoisson manifolds of Hydrodynamic type

Vincenzo Sciacca; Luca Degiovanni; Franco Magri

On deformation ofPoisson manifolds of Hydrodynamic type

Vincenzo Sciacca, Luca Degiovanni, Franco Magri

Matematica e Informatica

Risultato della ricerca: Article › peer review

37 Citazioni (Scopus)

Abstract

We study a class of deformations of infinite-dimensional Poisson manifoldsof hydrodynamic type which are of interest in the theory of Frobenius manifolds. Weprove 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 theabove manifolds.

Lingua originale	English
pagine (da-a)	1-24
Numero di pagine	24
Rivista	Communications in Mathematical Physics
Volume	253
Stato di pubblicazione	Published - 2005

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "We study a class of deformations of infinite-dimensional Poisson manifoldsof hydrodynamic type which are of interest in the theory of Frobenius manifolds. Weprove 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 theabove manifolds.",

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AU - Sciacca, Vincenzo

AU - Degiovanni, Luca

AU - Magri, Franco

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AB - We study a class of deformations of infinite-dimensional Poisson manifoldsof hydrodynamic type which are of interest in the theory of Frobenius manifolds. Weprove 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 theabove manifolds.

UR - http://hdl.handle.net/10447/28650

M3 - Article

VL - 253

SP - 1

EP - 24

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

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