Abstract
Any Spin (7)-manifold admits a metric connection ∇c with totally skew- symmetric torsion T c preserving the underlying structure. We classify those with ∇c-parallel T c ≠ 0 and non-Abelian isotropy algebra \({\mathfrak{iso}\,{\rm (T^c)}\,\leqslant\,\mathfrak{spin}\,{\rm (7)}}\) . These are isometric to either Riemannian products or homogeneous naturally reductive spaces, each admitting two ∇c-parallel spinor fields.
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Communicated by G. W. Gibbons
Supported by the SFB 647: ‘Space–Time–Matter’, German Research Foundation DFG.
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Puhle, C. Spin (7)-Manifolds with Parallel Torsion Form. Commun. Math. Phys. 291, 303–320 (2009). https://doi.org/10.1007/s00220-009-0879-0
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DOI: https://doi.org/10.1007/s00220-009-0879-0