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Hamiltonian 2-forms in Kahler geometry, I General Theory

Vestislav Apostolov·David M. J. Calderbank·Paul Gauduchon
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Abstract

We introduce the notion of a hamiltonian 2-form on a Kaehler manifold and obtain a complete local classification. This notion appears to play a pivotal role in several aspects of Kaehler geometry. In particular, on any Kaehler manifold with co-closed Bochner tensor, the (suitably normalized) Ricci form is hamiltonian, and this leads to an explicit description of these Kaehler metrics, which we call weakly Bochner-flat. Hamiltonian 2-forms draw attention to a general construction of Kaehler metrics which interpolates between toric geometry and Calabi-like constructions of metrics on (projective) line bundles. They also arise on conformally-Einstein Kaehler manifolds. We explore these connections and ramifications.

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BibTeXRIS

Vestislav Apostolov, David M. J. Calderbank, Paul Gauduchon. 2004-01-23. Hamiltonian 2-forms in Kahler geometry, I General Theory. https://arxiv.org/abs/math/0202280

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