Stability of certain Engel-like Distributions

TL;DR

This paper introduces a higher-dimensional analogue of Engel structures, inspired by Cartan prolongation, and investigates their stability properties, extending Gray's stability results for Engel manifolds.

Contribution

It presents a new higher-dimensional class of Engel-like structures and analyzes their stability, broadening understanding of geometric stability in contact-related manifolds.

Findings

Established stability criteria for the new structures

Extended Gray's stability theorem to higher dimensions

Provided foundational results for future research in Engel-like geometries

Abstract

In this article we introduce a higher dimensional analogue of Engel structure, motivated by the Cartan prolongation of contact manifolds. We study the stability of such structure, generalizing the Gray-type stability for Engel manifolds.