Quasi-Kähler Chern-flat manifolds and complex 2-step nilpotent Lie algebras
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 1, pp. 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.

Publié le :
Classification : 53C15, 53C55
Di Scala, Antonio J. 1 ; Lauret, Jorge 2 ; Vezzoni, Luigi 3

1 Dipartimento di Scienze Matematiche Politecnico di Torino Corso Duca degli Abruzzi, 24 10129 Torino, Italia
2 FaMAF and CIEM Universidad Nacional de Cordoba Ciudad Universitaria 5000 Córdoba, Argentina
3 Dipartimento di Matematica Università di Torino Via Carlo Alberto, 10 10123 Torino, Italia
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     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},
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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, Série 5, Tome 11 (2012) no. 1, pp. 41-60. http://www.numdam.org/item/ASNSP_2012_5_11_1_41_0/

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