On Legendrian foliations in contact manifolds I: Singularities and neighborhood theorems

Yang Huang
2015 Mathematical Research Letters  
In this note we study several aspects of coisotropic submanifolds of a contact manifold. In particular we give a structure theorem for the singularity of the characteristic foliation of a coisotropic submanifold. Moreover we establish the existence and uniqueness results of germs of contact structures near Legendrian foliations, which is a special case of coisotropic submanifold. This note can be thought of as an attempt to generalize the study of surfaces in three-dimensional contact geometry to higher dimensions.
doi:10.4310/mrl.2015.v22.n5.a6 fatcat:5cjl5c5qhjgwhjtdjmwbcl7maa