  The present work has a double aim. On the one hand we call attention on the
relationship existing between the Ashtekar formalism and other
gauge-theoretical approaches to gravity, in particular the Poincar\'e Gauge
Theory. On the other hand we study two kinds of solutions for the constraints
of General Relativity, consisting of two mutually independent parts, namely a
general three-metric-dependent contribution to the extrinsic curvature $K_{ab}$
in terms of the Cotton-York tensor, and besides it further metric independent
contributions, which we analyze in particular in the presence of isotropic
three-metrics.
