# Reduction and construction of Poisson quasi-Nijenhuis manifolds with background

## TL;DR

This paper extends Poisson reduction to quasi-Nijenhuis structures with background, introduces gauge transformations, and demonstrates their compatibility with reduction, enabling new constructions of such structures.

## Contribution

It introduces gauge transformations for Poisson quasi-Nijenhuis structures with background and proves their compatibility with reduction, expanding the theoretical framework.

## Key findings

- Gauge transformations preserve Poisson quasi-Nijenhuis structures with background.
- Compatibility of gauge transformations with the reduction process is established.
- New methods for constructing Poisson quasi-Nijenhuis structures are developed.

## Abstract

We extend the Falceto-Zambon version of Marsden-Ratiu Poisson reduction to Poisson quasi-Nijenhuis structures with background on manifolds. We define gauge transformations of Poisson quasi-Nijenhuis structures with background, study some of their properties and show that they are compatible with reduction procedure. We use gauge transformations to construct Poisson quasi-Nijenhuis structures with background.