On Legendrian foliations in contact manifolds II: Deformation theory

TL;DR

This paper investigates the deformation theory of coisotropic submanifolds with nonsingular characteristic foliations in contact manifolds, revealing connections to foliation theory and applying contact geometry to this context.

Contribution

It extends deformation theory of coisotropic submanifolds in contact manifolds and links it to foliation theory, building on structural theorems from prior work.

Findings

Deformation theory of coisotropic submanifolds is characterized under nonsingular characteristic foliations.

Connections between contact geometry and foliation theory are established.

Elementary applications of contact geometry to foliation theory are demonstrated.

Abstract

Using the structural theorems developed in [Hua13], we study the deformation theory of coisotropic submanifolds in contact manifolds, under the assumption that the characteristic foliation is nonsingular. In the "middle" dimensions, we find an interesting relationship with foliation theory. Some elementary applications of contact geometry in foliation theory are explored.