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Quasi-Kähler Chern-flat manifolds and complex 2-step nilpotent Lie algebras

    1. [1] Polytechnic University of Turin

      Polytechnic University of Turin

      Torino, Italia

    2. [2] Universidad Nacional de Córdoba

      Universidad Nacional de Córdoba

      Argentina

    3. [3] Università di Torino, Italia
  • Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 11, Nº 1, 2012, págs. 41-60
  • Idioma: inglés
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  • Resumen
    • 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-biinvariant almost complex structures on Lie algebras and bi-invariant complex structures. Some natural algebraic problems are approached and some exotic examples are carefully described.


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