  We study the metrics on the families of moduli spaces arising from probing
with a brane the ten and eleven dimensional supergravity solutions
corresponding to renormalisation group flows of supersymmetric large n gauge
theory. In comparing the geometry to the physics of the dual gauge theory, it
is important to identify appropriate coordinates, and starting with the case of
SU(n) gauge theories flowing from N=4 to N=1 via a mass term, we demonstrate
that the metric is Kahler, and solve for the Kahler potential everywhere along
the flow. We show that the asymptotic form of the Kahler potential, and hence
the peculiar conical form of the metric, follows from special properties of the
gauge theory. Furthermore, we find the analogous Kahler structure for the N=4
preserving Coulomb branch flows, and for an N=2 flow. In addition, we establish
similar properties for two eleven dimensional flow geometries recently
presented in the literature, one of which has a deformation of the conifold as
its moduli space. In all of these cases, we notice that the Kahler potential
appears to satisfy a simple universal differential equation. We prove that this
equation arises for all purely Coulomb branch flows dual to both ten and eleven
dimensional geometries, and conjecture that the equation holds much more
generally.
