On the characteristic connection of gwistor space

We give a brief presentation of gwistor spaces, which is a new concept from G ₂ geometry. Then we compute the characteristic torsion T ^c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and deduce the condition under which T ^c is ?^c-parallel; this allows for the classification of the G ₂ structure with torsion and the characteristic holonomy according to known references. The case of an Einstein base manifold is envisaged.