Engel structures on complex surfaces

Abstract

We classify complex surfaces $(M,J)$ admitting Engel structures $\mathcal{D}$ which are complex line bundles. Namely we prove that this happens if and only if $(M,J)$ has trivial Chern classes. We construct examples of such Engel structures by adapting a construction due to Geiges. We also study associated Engel defining forms and define a unique splitting of $TM$ associated with $\mathcal{D}$ $J$-Engel.

arXiv comment14 pages

References in corpus (1)

• The Engel-Lutz twist and overtwisted Engel structures