No CrossRef data available.
Article contents
Invariant scalar-flat Kähler metrics on line bundles over generalized flag varieties
Published online by Cambridge University Press: 13 May 2024
Abstract
Let G be a simply connected semisimple compact Lie group, let X be a simply connected compact Kähler manifold homogeneous under G, and let L be a negative holomorphic line bundle over X. We prove that all G-invariant Kähler metrics on the total space of L arise from the Calabi ansatz. Using this, we show that there exists a unique G-invariant scalar-flat Kähler metric in each G-invariant Kähler class of L. The G-invariant scalar-flat Kähler metrics are automatically asymptotically conical.
Keywords
MSC classification
- Type
- Article
- Information
- Copyright
- © The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society
Footnotes
This work is completed while the author is partly supported by graduate assistant fellowship in Graduate Center, CUNY, and also funded by the DFG under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure, and by the CRC 1442, Geometry: Deformations and Rigidity, of the DFG.