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Mathematics > Differential Geometry

arXiv:1811.08999 (math)
[Submitted on 22 Nov 2018 (v1), last revised 23 Dec 2020 (this version, v3)]

Title:Canonical Kähler metrics on classes of Lorentzian $4$-manifolds

Authors:Amir Babak Aazami, Gideon Maschler
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Abstract:Conditions for the existence of Kähler-Einstein metrics and central Kähler metrics [MS] 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 [AM] of Kähler metrics on such manifolds. The examples include both complete and incomplete metrics, and some reside on Lie groups associated to four types of Lie algebras. An appendix includes a similar construction for scalar-flat Kähler metrics.
Comments: sequel to [AM], final version. Various significant changes, in particular with regard to completeness
Subjects: Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
MSC classes: 53C25 (Primary) 53C50 53C55 (Secondary)
Cite as: arXiv:1811.08999 [math.DG]
  (or arXiv:1811.08999v3 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1811.08999
Journal reference: Ann. Global Anal. Geom. 57 (2020), no. 1, 175-204

Submission history

From: Gideon Maschler [view email]
[v1] Thu, 22 Nov 2018 02:52:39 UTC (20 KB)
[v2] Wed, 2 Jan 2019 16:02:22 UTC (22 KB)
[v3] Wed, 23 Dec 2020 14:51:00 UTC (40 KB)
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