Variations of gwistor space

TL;DR

This paper investigates natural variations of G2 structures on the unit tangent sphere bundle of 4-manifolds, identifying special structures and deriving related calibration equations.

Contribution

It introduces a family of G2 structures on tangent sphere bundles, highlighting the role of the original structure and deriving calibration and cocalibration conditions.

Findings

Identified a circle of G2 structures with the Sasaki metric.

Derived equations for calibration and cocalibration.

Analyzed special types like W3 pure and nearly-parallel.

Abstract

We study natural variations of the G2 structure {\sigma}_0 \in {\Lambda}^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.