Geodesic
Abelian complex structures on 6-dimensional compact nilmanifolds
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 2, pp. 215-229

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We classify the $6$-dimensional compact nilmanifolds that admit abelian complex structures, and for any such complex structure $J$ we describe the space of symplectic forms which are compatible with $J$.
Classification : 17B30, 53C15, 53C30, 53D05
Keywords: nilpotent Lie algebras; abelian complex structures; symplectic forms 
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     title = {Abelian complex structures on 6-dimensional compact nilmanifolds},
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Cordero, Luis A.; Fernández, Marisa; Ugarte, Luis. Abelian complex structures on 6-dimensional compact nilmanifolds. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 2, pp. 215-229. http://geodesic.mathdoc.fr/item/CMUC_2002__43_2_a2/