# Reduction of Nambu-Poisson manifolds by regular distributions

## TL;DR

This paper extends reduction theorems for Nambu-Poisson manifolds, showing reduction always occurs unless the distribution is zero, and introduces gauge transformations that commute with the reduction process.

## Contribution

It generalizes existing reduction theorems for Nambu-Poisson manifolds and introduces gauge transformations compatible with reduction.

## Key findings

- Reduction is always possible unless the distribution is zero.
- Extended Falceto-Zambon Poisson reduction to Nambu-Poisson manifolds.
- Gauge transformations commute with the reduction process.

## Abstract

The version of Marsden-Ratiu reduction theorem for Nambu-Poisson manifolds by a regular distribution has been studied by Ib$\acute{\text{a}}\tilde{\text{n}}$ez et al. In this paper we show that the reduction is always ensured unless the distribution is zero. Next we extend the more general Falceto-Zambon Poisson reduction theorem for Nambu-Poisson manifolds. Finally, we define gauge transformations of Nambu-Poisson structures and show that these transformations commute with the reduction procedure.