On the [formula omitted] bundle of a Riemannian 4-manifold

Abstract

We study the natural G 2 structure on the unit tangent sphere bundle S M of any given orientable Riemannian 4-manifold M , as was discovered in Albuquerque and Salavessa (2009,2010) [9,10]. A name is proposed for the space. We work in the context of metric connections, or so-called geometry with torsion, and describe the components of the torsion of the connection which imply certain equations of the G 2 structure. This article is devoted to finding the G 2 torsion tensors which classify our structure according to the theory in Fernandez and Gray (1982) [4].