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Deformations of Poisson-Nijenhuis strucures

Grant number: 22/02454-8
Support Opportunities:Research Grants - Visiting Researcher Grant - International
Duration: May 22, 2023 - June 21, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Igor Mencattini
Grantee:Igor Mencattini
Visiting researcher: Pedroni Marco
Visiting researcher institution: Università degli studi di Bergamo (Unibg), Italy
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil


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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