SU(3)-structures on quotients of 3-Sasakian orbifolds

Abstract

We show that if $(S,g,\xi_i,\eta_i,\Phi_i)$ is a quasi-regular $3$-Sasakian orbifold of dimension $7$, then its quotient $Z$ by one of the Reeb vector fields inherits an $SU(3)$-structure parametrized by two real parameters. We compute its torsion and show that it is an LT-structure. Moreover, for certain values of the parameters, we can provide a nearly K\"ahler structure on $Z$ appearing as a special case of our construction. We give several examples in the regular, quasi-regular and orbifold cases.