The concept of $Spin(7)$-instantons (Lewis 98) is an analogue of that of Yang-Mills instantons for SU(2)-principal connections on 4-dimensional manifolds, to (8-dimensional) Spin(7) manifolds.
On a Spin(7) manifold the differential 2-forms decompose into two irreducible representations, $\Lambda_7$ and $\Lambda_{21}$ under the action of Spin(7) (e.g. Lewis 98, p. 13).
A connection on the $Spin(7)$-manifold is called a $Spin(7)$-instanton it its curvature 2-form has vanishing component in the representation $\Lambda_7$ (Lewis 98, def.3.1).
C. Lewis, $Spin(7)$-Instantons, 1998 (pdf)
Simon Donaldson,Richard Thomas, Gauge theory in higher dimensions (pdf)
Naichung Conan Leung, Riemannian Geometry Over Different Normed Division Algebras, J. Differential Geom. Volume 61, Number 2 (2002), 289-333. (publisher page)
Last revised on January 22, 2016 at 16:48:28. See the history of this page for a list of all contributions to it.