Vanishing Ricci Tensor with Torsion

Question

Under what condition for the Torsion tensor does the Ricci Tensor vanish? I know that the Riemann Tensor is defined through: $$-R_{abc}^dV_d=\left(\nabla_a \nabla_b -\nabla_b \nabla_a \right)V_c-T^d_{ab}\nabla_dV_c$$ The Ricci Tensor is defined as: $$R_{ab}=R_{acb}^c$$ But I dont know how to find a condition on the Torsion tensor such that the Ricci Tensor vanishes.