Self-dual Yang-Mills fields and Ashtekar's variables

In the phase space of a complex SO(3) Yang-Mills theory, one may define the Yang-Mills Hamiltonian H_YM, which gives Yang-Mills theory, and Ashtekar's constraints, which give general relativity. The author looks for points on Ashtekar's constraint surface which stay on that surface under the evolution generated by H_YM. Such points exist for non-zero values of the cosmological constant; in general relativity, they correspond to self-dual spacetimes and, in Yang-Mills theory, to Yang-Mills fields which are self-dual with respect to a metric constructed algebraically from the Yang-Mills electric field.