Abstract
We introduce the notion of a hamiltonian 2-form on a Kahler manifold and obtain a complete local classification. This notion appears to play a pivotal role in several aspects of Kahler geometry. In particular, on any Kahler manifold with co-closed Bochner tensor, the (suitably normalized) Ricci form is hamiltonian, and this leads to an explicit description of these Kahler metrics, which we call weakly Bochner-flat. Hamiltonian 2-forms also arise on conformally Einstein Kahler manifolds and provide an Ansatz for extremal Kahler metrics unifying and extending many previous constructions.
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