I shall describe a theory of adiabatic response for controlled open systems governed by Lindblad evolutions. The theory gives quantum response a geometric interpretation induced from the geometry of Hilbert space projections. For a two level system the metric turns out to be the Fubini-Study metric and the symplectic form the adiabatic curvature. Nice things happen when the metric and symplectic structures are compatible so the space of controls is Kahler. I shall give examples of compatible physical systems. Work based on joint work with Fraas, Graf and Kenneth.