  Masur's divergence states that the horizontal foliation of translation
surfaces is uniquely ergodic if the geodesic flow is recurrent on the moduli
space. This established a relationship between geometrical properties of
foliations and the dynamics on the moduli space. In this paper, we extend this
theorem to complex torus and Kummer surfaces. We define and calculate
horizontal foliations and the corresponding geodesic flow in the moduli space
of K\"ahler metrics and prove that the horizontal foliation is uniquely ergodic
if the geodesic flow is recurrent. We also find the a necessary algebraic
condition on the geodesic flow for the horizontal foliation to be uniquely
ergodic.
