Cavalcanti, Gil R.; Gualtieri, Marco Generalized complex structures on nilmanifolds. (English) Zbl 1079.53106 J. Symplectic Geom. 2, No. 3, 393-410 (2004). This paper concerns classification of nilmanifolds \(M\) endowed with a so-called generalized complex strucure, (Hitchin), i.e., an almost complex structure \({\mathcal J}\) on the vector bundle \(\pi:E\equiv TM\oplus T^*M\to M\), such that it satisfies some further requirements: (i) \({\mathcal J}\) is orthogonal with respect to the natural inner product on sections of \(E\to M\); (ii) the \(+i\)-eigenbundle of \({\mathcal J}\) is required to be involutive with respect to the Courant bracket. In particular the authors specialize their investigation on \(6\)-dimensional nilmanifolds, where there exist some types without standard complex or symplectic structure. The results presented in this paper are obtained with standard techniques of almost complex bundles geometry. Reviewer: Agostino Prástaro (Roma) Cited in 59 Documents MSC: 53C56 Other complex differential geometry 53C30 Differential geometry of homogeneous manifolds Keywords:nilmanifolds; generalized complex structures × Cite Format Result Cite Review PDF Full Text: DOI arXiv