We classify complex surfaces (M,J) admitting Engel structures 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 D J-Engel.
Engel structures on complex surfaces
Pia N.;Placini G.
2021-01-01
Abstract
We classify complex surfaces (M,J) admitting Engel structures 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 D J-Engel.
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