On self-dual Yang-Mills fields on special complex surfaces

Abstract

We derive a generalization of the flat space Yang's and Newman's equations for self-dual Yang-Mills fields to (locally) conformally Kahler Riemannian 4-manifolds. The results also apply to Einstein metrics (whose full curvature is not necessarily self-dual). We analyse the possibility of hidden symmetries in the form of Backlund transformations, and we find a continuous group of hidden symmetries only for the case in which the geometry is conformally half-flat. No isometries are assumed.

13 pages

References in corpus (3)

• The Kinematic Algebra From the Self-Dual Sector
• Gravitational Instantons and special geometry
• Conformal geometry and half-integrable spacetimes