Hamiltonian 2-forms in Kahler geometry, I General Theory

Details Hamiltonian 2-forms in Kahler geometry, I General Theory Hamiltonian 2-forms in Kahler geometry, I General Theory

2002-02-26

arxiv.org/abs/math/0202280v2

J. Diff. Geom. 73 (2006) 359-412.

Mathematics

Differential Geometry

LaTeX, 41 pages; updated to improve exposition and coherence with part II (math.DG/0401320)

Scientific paper

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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