Deformations of Poisson-Nijenhuis strucures

• Grant number: 22/02454-8
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: May 22, 2023
• End date: 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

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)