  We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection
is constructed from the frame-field and (not necessarily compatible) spin
connection components. The fixed points of this flow include zero Yang-Mills
curvature configurations, for which the spin connection has zero torsion and
the associated Riemannian geometry is one of constant curvature. Perturbations
to the fixed point corresponding to hyperbolic 3-space can be expressed as a
linear superposition of distinct modes, some of which are exponentially growing
along the flow. The growing modes imply the divergence of the (gauge invariant)
perturbative torsion for a wide class of initial data, indicating an
instability of the background geometry that we confirm with numeric simulations
in the partially compactified case. There are stable modes with zero torsion,
but all the unstable modes are torsion-full. This leads us to speculate that
the instability is induced by the torsion degrees of freedom present in the
Yang-Mills flow.
