  The K\"ahler cone of a compact manifold carries a natural Riemannian metric,
given by the intersection product of its cohomology ring. We write down the
curvature tensor of this metric by embedding the K\"ahler cone in the space of
hermitian metrics on the underlying manifold. After discussing weak
functorality and completeness properties, we give a relative version of both
the K\"ahler cone and the metric.
