Cones of G manifolds and Killing spinors with skew torsion

Abstract

This paper is devoted to the systematic investigation of the cone construction for Riemannian $G$ manifolds M, endowed with an invariant metric connection with skew torsion ${\nabla }^c$, a `characteristic connection'. We show how to define a $\bar{G}$ structure on the cone $\bar M=M\x \R^+$ with a cone metric, and we prove that a Killing spinor with torsion on $M$ induces a spinor on $\bar{M}$ that is parallel w.\,r.\,t. the characteristic connection of the $\bar{G}$ structure. We establish the explicit correspondence between classes of metric almost contact structures on $M$ and almost hermitian classes on $\bar{M}$, resp. between classes of $G_2$ structures on $M$ and $\Spin(7)$ structures on $\bar{M}$. Examples illustrate how this `cone correspondence with torsion' works in practice.

36 pages; updated references & corrected typos

References in corpus (5)

• The Srni lectures on non-integrable geometries with torsion
• On types of non-integrable geometries
• The odd side of torsion geometry
• A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
• Dirac spectrum and spectral action of SU(3)