2017/06/28 by R.M.F. Coelho, Coelho, Rui, Nicola Pia +1
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1706.09306
openalex publication_date 2017/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A holomorphic Engel structure determines a flag of distributions W⊂ D⊂ E. We construct examples of Engel structures on C4 such that each of these distributions is hyperbolic in the sense that it has no tangent copies of C. We also construct two infinite families of pairwise non-isomorphic Engel structures on C4 by controlling the curves f:C→ C4 tangent to W. The first is characterised by the topology of the set of points in C4 admitting W-lines, and the second by a finer geometric property of this set. A consequence of the second construction is the existence of uncountably many non-isomorphic holomorphic Engel structures on C4.