Annals of Global Analysis and Geometry

, Volume 48, Issue 3, pp 269–294 | Cite as

Locally homogeneous nearly Kähler manifolds

  • V. CortésEmail author
  • J. J. Vásquez


We construct locally homogeneous six-dimensional nearly Kähler manifolds as quotients of homogeneous nearly Kähler manifolds M by freely acting finite subgroups of \({{\mathrm{Aut}}}_0(M)\). We show that non-trivial such groups do only exists if \(M=S^3\times S^3\). In that case, we classify all freely acting subgroups of \({{\mathrm{Aut}}}_0(M)=\text {SU}(2) \times \text {SU}(2) \times \text {SU}(2)\) of the form \(A\times B\), where \(A\subset \text {SU}(2) \times \text {SU}(2)\) and \(B\subset \text {SU}(2)\).


Nearly Kähler manifolds Locally homogeneous spaces Einstein manifolds 



This work was supported by the Collaborative Research Center SFB 676 “Particles, Strings, and the Early Universe” of the Deutsche Forschungsgemeinschaft.


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department Mathematik und Zentrum für Mathematische PhysikUniversität HamburgHamburgGermany
  2. 2.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

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