Spin(7)-manifolds with parallel torsion form

Abstract

Any Spin(7)-manifold admits a metric connection \nabla^c with totally skew-symmetric torsion T^c preserving the underlying structure. We classify those with \nabla^c-parallel T^c\neq0 and non-Abelian isotropy algebra iso(T^c)<spin(7). These are isometric to either Riemannian products or homogeneous naturally reductive spaces, each admitting two \nabla^c-parallel spinor fields.

16 pages, minor revision

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• Einstein warped G2 and Spin(7) manifolds
• A new $\frac{1}{2}$-Ricci type formula on the spinor bundle and applications