Rigidity of integral coisotropic submanifolds of contact manifolds

TL;DR

This paper studies integral coisotropic submanifolds in contact manifolds, showing they are rigid and have unobstructed deformations with discrete moduli, extending Legendrian submanifold theory.

Contribution

It identifies integral coisotropic submanifolds as a special class with rigidity and unobstructed deformation properties, generalizing Legendrian submanifolds in contact geometry.

Findings

Integral coisotropic submanifolds are rigid.

Deformation problem is unobstructed.

Moduli space is discrete.

Abstract

Unlike Legendrian submanifolds, the deformation problem of coisotropic submanifolds can be obstructed. Starting from this observation, we single out in the contact setting the special class of integral coisotropic submanifolds as the direct generalization of Legendrian submanifolds for what concerns deformation and moduli theory. Indeed, being integral coisotropic is proved to be a rigid condition, and moreover the integral coisotropic deformation problem is unobstructed with discrete moduli space.