Integrability of Reeb Distribution Associated to a Generalized Engel Manifold

In this paper, we define a generalized Reeb distribution of an Engel 4 n ‐manifold and give a necessary and sufficient condition for integrability of this Reeb distribution which gives a generalization of some results of N. Pia about Reeb distributions of Engel 4‐manifolds. Before that, we detailed explicit standard examples of Engel structure coming from the Cartan prolongation of some contact 3‐manifolds and 5‐manifolds.