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 [7]. We also study associated Engel defining forms and define a unique splitting of TM associated with \({\mathcal {D}}\) J-Engel.
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Notes
This means that it admits a finite orbifold cover with no cone points (see Section 7 in [21] for more details).
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Pia, N., Placini, G. Engel structures on complex surfaces. Annali di Matematica 200, 983–997 (2021). https://doi.org/10.1007/s10231-020-01022-0
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DOI: https://doi.org/10.1007/s10231-020-01022-0