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Annals of Global Analysis and Geometry

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

Locally homogeneous nearly Kähler manifolds

  • V. Cortés
  • J. J. Vásquez
Article

Abstract

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 \(B\subset \text {SU}(2)\).

Keywords

Nearly Kähler manifolds Locally homogeneous spaces Einstein manifolds 

Notes

Acknowledgments

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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Copyright information

© 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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