Non-existence of certain singularities in Legendrian foliations

Abstract

In this paper we show that the singular locus of a Legendrian foliation as defined in [Hua13] is a compact submanifold whose connected components are of codimension at most two. As a consequence, given any closed $(n+1)$-dimensional coisotropic submanifold $W$ in a contact $(2n+1)$-manifold, the contact structure in a sufficiently small neighborhood of $W$ is uniquely determined by the characteristic (Legendrian) foliation.

Cited by in corpus (2)

• Getting a handle on contact manifolds
• Existence of coLegendrians in contact $5$-manifolds