Cones of G manifolds and Killing spinors with skew torsion

الأصل · EN

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 ∇ᶜ, a `characteristic connection'. We show how to define a G structure on the cone M=M + with a cone metric, and we prove that a Killing spinor with torsion on M induces a spinor on M that is parallel w.r.t. the characteristic connection of the G structure. We establish the explicit correspondence between classes of metric almost contact structures on M and almost hermitian classes on M, resp. between classes of G₂ structures on M and (7) structures on M. Examples illustrate how this `cone correspondence with torsion' works in practice.