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arXiv · 0911.5655

Quasi-K\"ahler Chern-flat manifolds and complex 2-step nilpotent Lie algebras

Antonio J. Di Scala·Jorge Lauret·Luigi Vezzoni
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Abstract

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.

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Antonio J. Di Scala, Jorge Lauret, Luigi Vezzoni. 2009-11-30. Quasi-K\"ahler Chern-flat manifolds and complex 2-step nilpotent Lie algebras. https://arxiv.org/abs/0911.5655

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