G₂-Manifolds With Parallel Characteristic Torsion

2006/04/20 by Friedrich, Thomas · 3 citations
#53C25 #81T30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0604441

Abstract

We classify 7-dimensional cocalibrated \G₂-manifolds with parallel characteristic torsion and non-abelian holonomy. All these spaces admit a metric connection ∇^c with totally skew-symmetric torsion and a spinor field Ψ₁ solving the equations in the common sector of type II superstring theory. There exist \G₂-structures with parallel characteristic torsion that are not naturally reductive.

Cited by

• \mathrm G₂-structures with parallel skew-symmetric torsion
• Parallel torsion and G₂, Spin(7) instantons
• Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion

Related

• \mathrm G₂-structures with parallel skew-symmetric torsion
• Cocalibrated G₂-manifolds with Ricci flat characteristic connection
• The Srni lectures on non-integrable geometries with torsion
• Parallel torsion and G₂, Spin(7) instantons
• Cones of G manifolds and Killing spinors with skew torsion