The intrinsic torsion of SU(3) and G₂ structures

2002/02/26 by Simon Chiossi, Simon Salamon · 3 citations
Mathematics · #math.DG #msc:53C25 #msc:53C38

paper · pdf

published as Differential Geometry, Valencia 2001, World Sci. Publishing, 2002, pp 115-133 · Proc. conf. Differential Geometry Valencia 2001

arxiv created 2002/02/26 · arxiv updated 2009/11/30

Abstract

We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G₂ structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of a metric with holonomy G₂.

Cited by

• Parallel torsion and G₂, Spin(7) instantons
• Cohomologically calibrated affine connections and the Einstein condition on S² × T²
• Almost Calabi-Yau with torsion 6-manifolds and the instanton condition

Related

• SU(3)-structures on hypersurfaces of manifolds with G₂-structure
• Intrinsic torsion classes of Riemannian structures
• On the intrinsic torsion of spacetime structures
• \mathrm G₂-structures with parallel skew-symmetric torsion
• Generalized G₂-manifolds and SU(3)-structures