Abstract
We study natural variations of the \mathrm{G}_2 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 W_3 pure type and nearly-parallel type.
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