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arXiv · 1811.08999

Canonical K\"ahler metrics on classes of Lorentzian $4$-manifolds

Amir Babak Aazami·Gideon Maschler
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Abstract

Conditions for the existence of K\"ahler-Einstein metrics and central K\"ahler 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 K\"ahler 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 K\"ahler metrics.

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BibTeXRIS

Amir Babak Aazami, Gideon Maschler. 2018-11-22. Canonical K\"ahler metrics on classes of Lorentzian $4$-manifolds. https://arxiv.org/abs/1811.08999

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