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Locally homogeneous nearly Kähler manifolds

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

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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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Correspondence to V. Cortés.

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Cortés, V., Vásquez, J.J. Locally homogeneous nearly Kähler manifolds. Ann Glob Anal Geom 48, 269–294 (2015). https://doi.org/10.1007/s10455-015-9470-4

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