Variations of gwistor space

Abstract

We study natural variations of the G2 structure σ_0 \in 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 W3 pure type and nearly-parallel type.

16 pages

References in corpus (2)

• The Srni lectures on non-integrable geometries with torsion
• On the characteristic connection of gwistor space

Cited by in corpus (2)

• A fundamental differential system of Riemannian geometry
• A fundamental differential system of 3-dimensional Riemannian geometry