An involutivity theorem for a class of Poisson quasi-Nijenhuis manifolds

TL;DR

This paper extends the theory of Poisson quasi-Nijenhuis manifolds by presenting new involutivity theorems under specific factorization conditions, with applications to integrable systems.

Contribution

It introduces new deformation and involutivity theorems for Poisson quasi-Nijenhuis manifolds with factorized forms, expanding the theoretical framework.

Findings

New involutivity theorems for Poisson quasi-Nijenhuis manifolds

Examples demonstrating involutive structures in specific cases

Applications to classical integrable systems

Abstract

This note aims to continue our study about the applications of Poisson quasi-Nijenhuis geometry to the theory of classical completely integrable systems. More precisely, we will present new versions of the deformation and involutivity theorems, under the hypothesis that the closed 2-form triggering the deformation and the closed 3-form defining the Poisson quasi-Nijenhuis structure are factorized. These results will be supplemented by several examples of involutive Poisson quasi- Nijenhuis manifolds.