Abstract: In this talk I aim to give a non-technical introduction to some very technical work that I am currently doing with Vestislav Apostolov, David Calderbank and Paul Gauduchon (``ACG''). Weakly Bochner Flat Kahler metrics, which were introduced by ACG, are Kahler metrics whose normalized Ricci form is a so-called Hamiltonian 2-form. Such a form produces isometric Hamiltonian actions on the Kahler manifold. This means we have some local symmetry and if we form the Kahler quotient (which is also a symplectic quotient) we get a local description of the metric. One avenue to take after this is to try and extend the local description to a global one. Another avenue is to use the local description to construct new examples of Kahler metrics. These two avenues intersect and one of the aspects of the intersection is an awful lot of calculus.