Symplectic foliations induced by harmonic forms on 3-manifolds

TL;DR

This paper introduces a method to construct symplectic foliations on 3-manifolds using harmonic forms, linking geometric structures to topological approaches in solving Poisson's equation and gravity models.

Contribution

It presents a novel construction of symplectic foliations on 3-manifolds from harmonic forms, connecting geometry with topological methods in physics.

Findings

Constructed symplectic foliations from harmonic forms on 3-manifolds.

Proposed a topological approach to Poisson's equation.

Linked geometric structures to models of Newtonian gravity.

Abstract

This article details a construction of symplectic foliations on 3-dimensional orientable riemannian manifolds from harmonic forms; and how it suggests a topological approach to Poisson's equation and newtonian gravity.