  We consider the Yang-Mills equations for a matrix gauge group $G$ inside the
future light cone of 4-dimensional Minkowski space, which can be viewed as a
Lorentzian cone $C(H^3)$ over the 3-dimensional hyperbolic space $H^3$. Using
the conformal equivalence of $C(H^3)$ and the cylinder $R\times H^3$, we show
that, in the adiabatic limit when the metric on $H^3$ is scaled down, classical
Yang-Mills dynamics is described by geodesic motion in the infinite-dimensional
group manifold $C^\infty (S^2_\infty,G)$ of smooth maps from the boundary
2-sphere $S^2_\infty=\partial H^3$ into the gauge group $G$.
