The Reeb foliation arises as a family of Legendrian submanifolds at the end of a deformation of the standard S^3 in S^5

TL;DR

This paper constructs a deformation of the standard contact S^3 in S^5, showing how the Reeb foliation of S^3 naturally arises as a family of Legendrian submanifolds within S^5.

Contribution

It introduces a novel deformation process of S^3 in S^5 that reveals the Reeb foliation as a family of Legendrian submanifolds, linking foliation theory with contact geometry.

Findings

Reeb foliation realized as Legendrian submanifolds in S^5

Deformation of standard S^3 into Reeb foliation

Connection between foliation and contact geometry

Abstract

We realize the Reeb foliation of S^3 as a family of Legendrian submanifolds of the unit S^5 \subset C^3, Moreover we construct a deformation of the standard contact S^3 in S^5, via a family of contact submanifolds, into this realization.