REDUCTIONS BY ISOMETRIES OF THE SELF-DUAL YANG-MILLS EQUATIONS IN 4-DIMENSIONAL EUCLIDEAN-SPACE

A classification of the subgroups of the four-dimensional Euclidean gr oup is given. The (anti-) self-dual Yang-Mills equations in four-dimen sional Euclidean space are then reduced for each class representative and for any gauge group when a strict invariance of the gauge fields i s required, or for the gauge group SO(3) if the gauge fields remain in variant up to gauge transformations. Amongst the residual systems, man y constitute sets of first order ordinary differential equations shari ng the Painleve property.