, Volume 143, Issue 1, pp 101-122

A classification of Riemannian manifolds with structure group Spin (7)

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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.