Mathematics
Canonical Kähler metrics on classes of Lorentzian 4-manifolds
Document Type
Article
Abstract
Conditions for the existence of Kähler–Einstein metrics and central Kähler metrics (Maschler in Trans Am Math Soc 355:2161–2182, 2003) along with examples, both old and new, are given on classes of Lorentzian 4-manifolds with two distinguished vector fields. The results utilize the general construction (Aazami and Maschler in Kähler metrics via Lorentzian geometry in dimension four, Complex Manifolds 7:36–61 (2020) of Kähler metrics on such manifolds. The examples include both complete and incomplete metrics, and some reside on Lie groups associated with four types of Lie algebras. An appendix includes a similar construction for scalar-flat Kähler metrics.
Publication Title
Annals of Global Analysis and Geometry
Publication Date
2-2020
Volume
57
Issue
1
First Page
175
Last Page
204
ISSN
0232-704X
DOI
10.1007/s10455-019-09694-5
Keywords
Central Kahler metric, complete metric, conformal, Kähler, Kähler-Einstein, Lorentzian metric
Repository Citation
Aazami, Amir Babak and Maschler, Gideon, "Canonical Kähler metrics on classes of Lorentzian 4-manifolds" (2020). Mathematics. 24.
https://commons.clarku.edu/mathematics/24
