Journal of Differential Geometry

Hamiltonian 2-Forms in Kähler Geometry, I General Theory

Vestislav Apostolov, David M.J. Calderbank, and Paul Gauduchon

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

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J. Differential Geom. Volume 73, Number 3 (2006), 359-412.

First available in Project Euclid: 27 April 2006

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Apostolov, Vestislav; Calderbank, David M.J.; Gauduchon, Paul. Hamiltonian 2-Forms in Kähler Geometry, I General Theory. J. Differential Geom. 73 (2006), no. 3, 359--412. doi:10.4310/jdg/1146169934.

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