YANG-MILLS FIELDS WHICH ARE NOT SELF-DUAL

The purpose of this paper is to prove the existence of a new family of non-self-dual finite-energy solutions to the Yang-Mills equations on Euclidean four-space, with SU(2) as a guage group. The approach is that of "equivariant geometry:" attention is restricted to a special class of fields, those that satisfy a certain kind of rotational symmetry, for which it is proved that (1) a solution to the Yang-Mills equations exists among them; and (2) no solution to the self-duality equations exists among them. The first assertion is proved by an application of the direct method of the calculus of variations (existence and regularity of minimizers), and the second assertion by studying the symmetry properties of the linearized self-duality equations. The same technique yields a new family of non-self-dual solutions on the complex projective plane.