  We give an SU(2) covariant representation of the constraints of Euclidean
general relativity in the Ashtekar variables. The guiding principle is the use
of triads to transform all free spatial indices into SU(2) indices. A central
role is played by a special covariant derivative. The Gauss, diffeomorphism and
Hamiltonian constraints become purely algebraic restrictions on the curvature
and the torsion associated with this connection. We introduce coordinates on
the jet space of the dynamical fields which cleanly separate the constraint and
gauge directions from the true physical directions. This leads to a
classification of all local diffeomorphism and Gauss invariant charges.
