The Engel–Lutz twist and overtwisted Engel structures

Engel structures on complex surfaces

“…This problem was solved positively for the first time in [20]. The later works [4,16] established an existence h-principle and constructed a flexible (in the sense of Gromov) family of Engel structures. Definition 2.2 Let (M 4 , J) be an almost complex manifold, a J-Engel structure D is an Engel structure such that JD = D.…”

“…[D, D] = E and [D, E] = TM . These objects were discovered a long time ago [3,6], and recent developments have sparked new interest in the field [4,16,20].…”

Analytic Torsion of Generic Rank Two Distributions in Dimension Five

“…The question to what extent generic rank two distributions abide by an h-principle [ 45 , 51 ] has served as a motivation for us to study the analytic torsion of the associated Rumin complex, cf. [ 10 , 30 , 31 , 41 , 44 , 48 , 97 ].…”