On deformation ofPoisson manifolds of Hydrodynamic type

Vincenzo Sciacca, Luca Degiovanni, Franco Magri

Research output: Contribution to journalArticlepeer-review

37 Citations (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.
Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalCommunications in Mathematical Physics
Volume253
Publication statusPublished - 2005

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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