Mathematics
On the Completeness of Some Bianchi Type A and Related Kähler–Einstein Metrics
Document Type
Article
Abstract
We prove the existence of complete cohomogeneity one triaxial Kähler–Einstein metrics in dimension four under an action of the Euclidean group E(2). We also demonstrate local existence of Ricci flat Kähler metrics of a related type that are given via generalized PDEs, and determine, under mild conditions, whether they are complete. The common framework for both metric types is a frame-dependent system of Lie bracket relations and generalized PDEs yielding a class of Kähler–Einstein metrics on 4-manifolds which includes all diagonal Bianchi type A metrics.
Publication Title
Journal of Geometric Analysis
Publication Date
8-2021
Volume
31
Issue
8
First Page
8347
Last Page
8384
ISSN
1050-6926
DOI
10.1007/s12220-020-00597-7
Keywords
Bianchi type A, cohomogeneity one metrics, Kähler–Einstein metrics
Repository Citation
Maschler, Gideon and Ream, Robert, "On the Completeness of Some Bianchi Type A and Related Kähler–Einstein Metrics" (2021). Mathematics. 30.
https://commons.clarku.edu/mathematics/30
