Quasi-Kähler Chern-flat manifolds and complex 2-step nilpotent Lie algebras
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 1, p. 41-60

The study of quasi-Kähler Chern-flat almost Hermitian manifolds is strictly related to the study of anti-bi-invariant almost complex Lie algebras. In the present paper we show that quasi-Kähler Chern-flat almost Hermitian structures on compact manifolds are in correspondence to complex parallelisable Hermitian structures satisfying the second Gray identity. From an algebraic point of view this correspondence reads as a natural correspondence between anti-bi-invariant almost complex structures on Lie algebras and bi-invariant complex structures. Some natural algebraic problems are approached and some exotic examples are carefully described.

Published online : 2018-06-21
Classification:  53C15,  53C55
@article{ASNSP_2012_5_11_1_41_0,
     author = {Di Scala, Antonio J. and Lauret, Jorge and Vezzoni, Luigi},
     title = {Quasi-K\"ahler Chern-flat manifolds and complex $2$-step nilpotent Lie algebras},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 11},
     number = {1},
     year = {2012},
     pages = {41-60},
     zbl = {1252.53038},
     mrnumber = {2953044},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2012_5_11_1_41_0}
}
Di Scala, Antonio J.; Lauret, Jorge; Vezzoni, Luigi. Quasi-Kähler Chern-flat manifolds and complex $2$-step nilpotent Lie algebras. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 1, pp. 41-60. http://www.numdam.org/item/ASNSP_2012_5_11_1_41_0/

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