  The Gauss law constraint in the Hamiltonian form of the $SU(2)$ gauge theory
of gluons is satisfied by any functional of the gauge invariant tensor variable
$\phi^{ij} = B^{ia} B^{ja}$. Arguments are given that the tensor $G_{ij} =
(\phi^{-1})_{ij}\,\det B$ is a more appropriate variable. When the Hamiltonian
is expressed in terms of $\phi$ or $G$, the quantity $\Gamma^i_{jk}$ appears.
The gauge field Bianchi and Ricci identities yield a set of partial
differential equations for $\Gamma$ in terms of $G$. One can show that $\Gamma$
is a metric-compatible connection for $G$ with torsion, and that the curvature
tensor of $\Gamma$ is that of an Einstein space. A curious 3-dimensional
spatial geometry thus underlies the gauge-invariant configuration space of the
theory, although the Hamiltonian is not invariant under spatial coordinate
transformations. Spatial derivative terms in the energy density are singular
when $\det G=\det B=0$. These singularities are the analogue of the centrifugal
barrier of quantum mechanics, and physical wave-functionals are forced to
vanish in a certain manner near $\det B=0$. It is argued that such barriers are
an inevitable result of the projection on the gauge-invariant subspace of the
Hilbert space, and that the barriers are a conspicuous way in which non-abelian
gauge theories differ from scalar field theories.
