On the characteristic connection of gwistor space

Abstract

We give a brief presentation of gwistor space, which is a new concept from G2 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 G2 structure with torsion and the characteristic holonomy according to known references. The case with the Einstein base manifold is envisaged.