Cones of G manifolds and Killing spinors with skew torsion

2013/03/14 by Ilka Agricola, Agricola, Ilka, Jos Höll +1 · 1 citation
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.1303.3601

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 ∇^c, a `characteristic connection'. We show how to define a G structure on the cone M=M\x \R<sup>+</sup> 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 G<sub>2</sub> structures on M and \Spin(7) structures on M. Examples illustrate how this `cone correspondence with torsion' works in practice.

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