  A Kahler metric is said to be Bochner-Kahler if its Bochner curvature
vanishes. This is a nontrivial condition when the complex dimension of the
underlying manifold is at least 2. In this article it will be shown that, in a
certain well-defined sense, the space of Bochner-Kahler metrics in complex
dimension n has real dimension n+1 and a recipe for an explicit formula for any
Bochner-Kahler metric will be given.
  It is shown that any Bochner-Kahler metric in complex dimension n has local
(real) cohomogeneity at most n. The Bochner-Kahler metrics that can be
`analytically continued' to a complete metric, free of singularities, are
identified. In particular, it is shown that the only compact Bochner-Kahler
manifolds are the discrete quotients of the known symmetric examples. However,
there are compact Bochner-Kahler orbifolds that are not locally symmetric. In
fact, every weighted projective space carries a Bochner-Kahler metric.
  The fundamental technique is to construct a canonical infinitesimal torus
action on a Bochner-Kahler metric whose associated momentum mapping has the
orbits of its symmetry pseudo-groupoid as fibers.
