Locally homogeneous nearly Kähler manifolds

Abstract

We construct locally homogeneous 6-dimensional nearly Kähler manifolds as quotients of homogeneous nearly Kähler manifolds $M$ by freely acting finite subgroups of $Au{t}_0(M)$. 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 $Au{t}_0(M)=SU(2)\times SU(2)\times SU(2)$ of the form $A\times B$, where $A\subset SU(2)\times SU(2)$ and $B\subset SU(2)$.

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• When is the (co)sine of a rational angle equal to a rational number?
• Half-BPS M2-brane orbifolds