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Annals of Global Analysis and Geometry

, Volume 42, Issue 2, pp 147–170 | Cite as

Homogeneous nearly Kähler manifolds

  • J. C. González Dávila
  • F. Martín CabreraEmail author
Article

Abstract

The structure of nearly Kähler manifolds was studied by Gray in several articles, mainly in Gray (Math Ann 223:233–248, 1976). More recently, a relevant progress on the subject has been done by Nagy. Among other results, he proved that a complete strict nearly Kähler manifold is locally a Riemannian product of homogeneous nearly Kähler spaces, twistor spaces over quaternionic Kähler manifolds and six-dimensional (6D) nearly Kähler manifolds, where the homogeneous nearly Kähler factors are also 3-symmetric spaces. In the present article, we show some further properties relative to the structure of nearly Kähler manifolds and, using the lists of 3-symmetric spaces given by Wolf and Gray, we display the exhaustive list of irreducible simply connected homogeneous strict nearly Kähler manifolds. For such manifolds, we give details relative to the intrinsic torsion and the Riemannian curvature.

Keywords

Nearly Kähler Homogeneous space 3-Symmetric space Intrinsic torsion Minimal connection 

Mathematics Subject Classification (2000)

53C20 53C30 53C22 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • J. C. González Dávila
    • 1
  • F. Martín Cabrera
    • 2
    Email author
  1. 1.Department of Fundamental MathematicsUniversity of La LagunaLa Laguna, TenerifeSpain
  2. 2.Department of Fundamental Mathematics, CSIC Associated UnityUniversity of La LagunaLa Laguna, TenerifeSpain

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