Spin(7)-manifolds with three-torus symmetry
  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. 
Thomas Bruun Madsen
math.DG hep-th