Forme semi-locale des feuilletages legendriens

TL;DR

This paper establishes a semi-local canonical form for Legendrian foliations near Legendrian submanifolds in contact manifolds, generalizing previous local results and introducing a cohomology class that measures obstructions.

Contribution

It generalizes local Legendrian foliation results to a semi-local setting and introduces a cohomology to analyze obstructions to flatness.

Findings

Provides a semi-local canonical form for Legendrian foliations.

Introduces a cohomology class that obstructs flatness.

Extends local results by Libermann and Pang to a semi-local context.

Abstract

We describe a semi-local canonical form for Legendrian foliations on contact manifolds in the neighbourhood of a Legendrian submanifold. This result generalizes local results by Libermann and Pang on Legendrian foliations on contact manifolds, and is analogeous to a semi-local result by Weinstein in the symplectic case. For the proof, we introduce and use a class of cohomology that obstructs the possibility to make a Legendrian foliation flat.