High Quality Content by WIKIPEDIA articles! In mathematics, a Spin(7)-manifold is an eight-dimensional Riemannian manifold with the exceptional holonomy group Spin(7). Spin(7)-manifolds are Ricci-flat and admit a parallel spinor. They also admit a parallel 4-form, known as the Cayley form, which is a calibrating form for a special class of submanifolds called Cayley cycles. The deformation theory of such submanifolds was first investigated by R. McLean. Examples of complete Spin(7)-metrics on non-compact manifolds were first constructed by Bryant and Salamon The first examples of compact Spin(7)-manifolds were constructed by Dominic Joyce.

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