Hamiltonian 2-Forms in Kähler Geometry, I General Theory

By V. Apostolov, D. Calderbank, P. Gauduchon. 2002

151 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Geometry and Topology, Surgery

View Paper: https://www.semanticscholar.org/paper/9d40129d3ed5143d912283347ae34a7eef39b287

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In Applied Mathematics

1. J. Sparks
2. D. Martelli
3. J. Gauntlett
4. D. Waldram
5. Christina W. Tønnesen-Friedman
6. P. Gauduchon
7. D. Calderbank
8. V. Apostolov

In Geometry and Topology

1. J. Sparks
2. D. Martelli
3. J. Gauntlett
4. D. Waldram
5. Christina W. Tønnesen-Friedman
6. Alberto Zaffaroni
7. P. Gauduchon
8. D. Calderbank

In Surgery

1. Christina W. Tønnesen-Friedman
2. V. Apostolov
3. D. Calderbank
4. P. Gauduchon

Citations in the corpus

• Toric Sasaki-Einstein metrics on S2 × S3 (2004, background): “are given in explicit form in reference [ 11 ].”
• Hamiltonian 2-forms in Kähler geometry, III extremal metrics and stability (2005, methodology): “To prove the claim, we use the theory of hamiltonian 2-forms of order 1 from [4, 5].”