Self-duality and integrable systems
We consider the total space of self-dual connections and self-dual (i.e. the Weyl curvature is self-dual) metrics on a four-manifold. An infinite dimensional Lie algebra acts on this space transitively. Especially coordinate transformations of the corresponding twistor space act on the space of self-dual metrics, and gauge transformations act on the space of self-dual connections. In this sense composed systems of self-dual connections and self-dual metrics are completely integrable, and this integrability is equivalent to the integrability of complex structures of twistor spaces. This system can be considered as a deformation of D-modules in higher dimensions.
scientific article; zbMATH DE number 4205447