  Renormalisation Group (RG) flows in theory space (the space of couplings) are
generated by a vector field -- the $\beta$ function. Using a specific metric
ansatz in theory space and certain methods employed largely in the context of
General Relativity, we examine the nature of the expansion, shear and rotation
of geodesic RG flows. The expansion turns out to be a negative quantity
inversely related to the norm of the $\beta$ function. This implies the
focusing of the flows towards the fixed points of a given field theory. The
evolution equation for the expansion along geodesic RG flows is written down
and analysed. We illustrate the results for a scalar field theory with a
$j\phi$ coupling and pointers to other areas are briefly mentioned.
