1997/04/02 by Maxim Kazarian, Kazarian, Maxim, Richard Montgomery +3
Computer Science · Mathematics · #58A30 #Differential Equations and Numerical Methods #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.dg-ga/9704001
openalex publication_date 1997/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There is a remarkable type of field of two-planes special to four dimensions known as an Engel distributions. They are the only stable regular distributions besides the contact, quasi-contact and line fields. If an arbitrary two-plane field on a four-manifold is slightly perturbed then it will be Engel at generic points. On the other hand, if a manifold admits an oriented Engel structure then the manifold must be parallelizable and consequently the alleged Engel distribution must have a degeneration loci -- a point set where the Engel conditions fails. By a theorem of Zhitomirskii this locus is a finite union of surfaces. We prove that these surfaces represent Chern classes associated to the distribution.