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arXiv · 1906.12212

Engel structures on complex surfaces

Nicola Pia·Giovanni Placini
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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.

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Nicola Pia, Giovanni Placini. 2019-06-28. Engel structures on complex surfaces. https://doi.org/10.1007/s10231-020-01022-0

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