%0 Journal Article
%T Quasi-K£¿hler Chern-flat manifolds and complex 2-step nilpotent Lie algebras
%A Antonio J. Di Scala
%A Jorge Lauret
%A Luigi Vezzoni
%J Mathematics
%D 2009
%I arXiv
%X The study of quasi-K\"ahler 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-K\"ahler 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 to bi-invariant complex structures. Some natural algebraic problems are approached and some exotic examples are carefully described.
%U http://arxiv.org/abs/0911.5655v3