Locally homogeneous nearly K\"ahler manifolds

Abstract

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 $Aut_0(M)$. 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 $Aut_0(M)=SU (2) \times SU (2) \times SU (2)$ of the form $A\times B$, where $A\subset SU (2) \times SU (2)$ and $B\subset SU (2)$.