On the G_2 bundle of a Riemannian 4-manifold

Abstract

We study the natural G_2 structure on the unit tangent sphere bundle SM of any given orientable Riemannian 4-manifold M, as it was discovered in \cite{AlbSal}. 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 \cite{FerGray}.

Completely improved, new examples, 26 pages

References in corpus (4)

• Killing spinor equations in dimension 7 and geometry of integrable G_2-manifolds
• The Srni lectures on non-integrable geometries with torsion
• Geometric structures of vectorial type
• The G_2 sphere over a 4-manifold

Cited by in corpus (7)

• Homotheties and topology of tangent sphere bundles
• Weighted metrics on tangent sphere bundles
• Variations of gwistor space
• A fundamental differential system of Riemannian geometry
• A fundamental differential system of 3-dimensional Riemannian geometry
• On the characteristic connection of gwistor space
• Isometries and curvatures of tangent sphere bundles