, 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 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.
- Dominic Joyce (2000). Compact Manifolds with Special Holonomy. Oxford University Press. ISBN 0-19-850601-5.