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Deformations of Poisson-Nijenhuis strucures

Abstract

The aim of this project is to investigate the deformations of Poisson- Nijenhuis structures induced by a two-form satisfying a suitable integrability condition. From a strictly geometrical point of view these deformations are naturally related to the gauge transformations of the Dirac structures underlying the original Poisson- Nijenhuis manifold. On the other hand from the view point of mathematical physics they are expected to relate different integrable systems, as it is exemplified in [FMOP] and [FMP], where it was investigated the relation between the close and the open Toda system from this perspective and where it was analyzed the deformation of the canonical PN structures. (AU)

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