Open Access
July 2006 Hamiltonian 2-Forms in Kähler Geometry, I General Theory
Vestislav Apostolov, David M.J. Calderbank, Paul Gauduchon
J. Differential Geom. 73(3): 359-412 (July 2006). DOI: 10.4310/jdg/1146169934


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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Vestislav Apostolov. David M.J. Calderbank. Paul Gauduchon. "Hamiltonian 2-Forms in Kähler Geometry, I General Theory." J. Differential Geom. 73 (3) 359 - 412, July 2006.


Published: July 2006
First available in Project Euclid: 27 April 2006

zbMATH: 1101.53041
MathSciNet: MR2228318
Digital Object Identifier: 10.4310/jdg/1146169934

Rights: Copyright © 2006 Lehigh University

Vol.73 • No. 3 • July 2006
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