Journal of Differential Geometry

Hamiltonian 2-Forms in Kähler Geometry, I General Theory

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

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 27 April 2006

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1146169934

Digital Object Identifier
doi:10.4310/jdg/1146169934

Mathematical Reviews number (MathSciNet)
MR2228318

Zentralblatt MATH identifier
1101.53041

Citation

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. https://projecteuclid.org/euclid.jdg/1146169934


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