A rigidity result for coisotropic submanifolds in contact geometry

We study coisotropic deformations of a compact regular coisotropic submanifold C in a contact manifold \((M,\xi )\) $(M,\xi )$ . Our main result states that C is rigid among nearby coisotropic submanifolds whose characteristic foliation is diffeomorphic to that of C. When combined with a classical rigidity result for foliations, this yields conditions under which C is rigid among all nearby coisotropic submanifolds.