Mathematical Research Letters

Volume 22 (2015)

Number 5

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

Pages: 1373 – 1400

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n5.a6

Author

Yang Huang (Max-Planck-Institut für Mathematik, Bonn, Germany)

Abstract

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 paper can be thought of as an attempt to generalize the study of surfaces in three-dimensional contact geometry to higher dimensions.

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Published 13 April 2016