A smooth codimension-one foliation of the five-sphere by symplectic leaves

TL;DR

This paper constructs a smooth codimension-one foliation on the five-sphere with symplectic four-manifold leaves, demonstrating the existence of a regular Poisson structure on the five-sphere.

Contribution

It introduces a novel foliation of the five-sphere with symplectic leaves, establishing a new example of a regular Poisson structure in five dimensions.

Findings

Existence of a smooth foliation with symplectic leaves on the five-sphere

Construction of a complete regular Poisson structure on the five-sphere

Smooth variation of symplectic structures across leaves

Abstract

We construct a smooth codimension-one foliation on the five-sphere in which every leaf is a symplectic four-manifold and such that the symplectic structure varies smoothly. Our construction implies the existence of a complete regular Poisson structure on the five-sphere.