Singular multicontact structures

TL;DR

This paper studies automorphisms of singular multicontact structures, generalizing Martinet distributions, and introduces finite type singularities with extension results for para-CR functions.

Contribution

It characterizes automorphisms of singular multicontact structures and introduces the concept of finite type singularities in para-CR geometry.

Findings

Automorphisms of singular multicontact structures are described.

Extension results for para-CR functions and mappings are established.

Finite type singularities are defined and analyzed.

Abstract

We describe the automorphisms of a singular multicontact structure, that is a generalisation of the Martinet distribution. Such a structure is interpreted as a para-CR structure on a hypersurface M of a direct product space R^2 x R^2. We introduce the notion of a finite type singularity analogous to CR geometry and, along the way, we prove extension results for para-CR functions and mappings on embedded para-CR manifolds into the ambient space.