Variations of gwistor space

We study natural variations of the G 2 structure σ 0 ∈ Λ 3 + existing on the unit tangent sphere bundle SM of any oriented Riemannian 4-manifold M . We find a circle of structures for which the induced metric is the usual one, the so-called Sasaki metric, and prove how the original structure has a preferred role in the theory. We deduce the equations of calibration and cocalibration, as well as those of W 3 pure type and nearly-parallel type