Summary
Riemannian manifolds with structure group Spin (7)are 8-dimensional and have a distinguished 4 -form. In this paper, the covariant derivative of the fundamental 4 -form is studied, and it is shown that there are precisely four classes of such manifolds.
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Fernández, M. A classification of Riemannian manifolds with structure group Spin (7). Annali di Matematica pura ed applicata 143, 101–122 (1986). https://doi.org/10.1007/BF01769211
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DOI: https://doi.org/10.1007/BF01769211