Locally homogeneous nearly K\"ahler manifolds

We construct locally homogeneous 6-dimensional nearly K"ahler manifolds as quotients of homogeneous nearly K"ahler 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 $B\subset SU(2)$.