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arXiv · 0807.4875

Spin(7)-manifolds with parallel torsion form

Christof Puhle
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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.

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Christof Puhle. 2008-11-17. Spin(7)-manifolds with parallel torsion form. https://doi.org/10.1007/s00220-009-0879-0

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