On splitting of exact differential forms

TL;DR

This paper explores the internal structure of de Rham cohomology and examines phase flows in three-dimensional space with Nambu Poisson structures, providing insights into their mathematical properties.

Contribution

It introduces a new analysis of the internal structure of de Rham cohomology and applies it to phase flows with Nambu Poisson structures in three dimensions.

Findings

Detailed analysis of de Rham cohomology structure

Examples of phase flows with Nambu Poisson structure in R^3

Insights into the geometric properties of differential forms

Abstract

In work the internal structure of de Rham cohomology is considered. As examples the phase flows in $\mathbb {R}^3$ admitting the Nambu Poisson structure are studied.