On deformations of coisotropic submanifolds with fixed characteristic foliation

TL;DR

This paper demonstrates that restricting coisotropic deformations to those preserving the characteristic foliation's diffeomorphism type removes obstructions, extending previous unobstructedness results.

Contribution

It introduces a condition on deformations of coisotropic submanifolds that ensures unobstructedness by fixing the characteristic foliation.

Findings

Deformations with fixed characteristic foliation are unobstructed.

Extends Ruan's unobstructedness result to a broader class of coisotropic submanifolds.

Shows the importance of foliation-preserving conditions in deformation theory.

Abstract

It is well-known that the deformation problem of a compact coisotropic submanifold $C$ in a symplectic manifold is obstructed in general. We show that it becomes unobstructed if one only allows coisotropic deformations whose characteristic foliation is diffeomorphic to that of $C$. This extends an unobstructedness result in the setting of integral coisotropic submanifolds due to Ruan.