  Riemannian geometry in four dimensions naturally leads to an SL(3) connection
that annihilates a basis for self-dual two-forms. Einstein's equations may be
written in terms of an SO(3) connection, with SO(3) chosen as an appropriate
subgroup of SL(3). We show how a set of "neighbours" of Einstein's equations
arises because the subgroup may be chosen in different ways. An explicit
example of a non-Einstein metric obtained in this way is given. Some remarks on
three dimensional space-times are made.
