Engel structures on and are studied in this paper, where is a –dimensional manifold. We suppose that these structures have characteristic line fields parallel to the fibres, or . It is proved that they are characterized by contact structures on the cross section , the twisting numbers, and Legendrian foliations on both ends in the case of .
"Engel structures with trivial characteristic foliations." Algebr. Geom. Topol. 2 (1) 239 - 255, 2002. https://doi.org/10.2140/agt.2002.2.239