  Partial connections are (singular) differential systems generalizing
classical connections on principal bundles, yielding analogous decompositions
for manifolds with nonfree group actions. Connection forms are interpreted as
maps determining projections of the tangent bundle onto the partial connection;
this approach eliminates many of the complications arising from the presence of
isotropy. A connection form taking values in the dual of the Lie algebra is
smooth even at singular points of the action, while analogs of the classical
algebra-valued connection form are necessarily discontinuous at such points.
The curvature of a partial connection form can be defined under mild technical
hypotheses; the interpretation of curvature as a measure of the lack of
involutivity of the (partial) connection carries over to this general setting.
