Spin(7)-manifolds with three-torus symmetry

Preprint number: CP3-Origins-2011-9
Author: Thomas Bruun Madsen (CP3-Origins)
External link: arXiv.org

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Metrics of exceptional holonomy are vacuum solutions to the Einstein equation. In this paper we describe manifolds with holonomy contained in Spin(7) preserved by a three-torus symmetry in terms of tri-symplectic geometry of four-manifolds. These complement examples that have appeared in the context of domain wall problems in supergravity.