Duality and Yang–Mills fields on quaternionic Kähler manifolds

Abstract

The concept of a self-dual connection on a four-dimensional Riemannian manifold is generalized to the 4n-dimensional case of any quaternionic Kähler manifold. The generalized self-dual connections are minima of a modified Yang–Mills functional. It is shown that our definitions give a correct framework for a mapping theory of quaternionic Kähler manifolds. The mapping theory is closely related to the construction of Yang–Mills fields on such manifolds. Some monopole-like equations are discussed.