Classification of left-invariant Einstein metrics on $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ that are bi-invariant under a one-parameter subgroup

Vicente Cortés; Jeremias Ehlert; Alexander S. Haupt; David Lindemann

Classification of left-invariant Einstein metrics on $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ that are bi-invariant under a one-parameter subgroup

Differential Geometry 2022-01-20 v1 High Energy Physics - Theory Mathematical Physics math.MP

Authors: Vicente Cortés , Jeremias Ehlert , Alexander S. Haupt , David Lindemann

Abstract

We classify all left-invariant pseudo-Riemannian Einstein metrics on $\mathrm{SL}(2,\mathbb{R})\times \mathrm{SL}(2,\mathbb{R})$ that are bi-invariant under a one-parameter subgroup. We find that there are precisely two such metrics up to homothety, the Killing form and a nearly pseudo-K\"ahler metric.

Keywords

left-invariant metrics einstein metrics pseudo-riemannian sl(2,r) bi-invariant one-parameter subgroup

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@article{arxiv.2201.07343,
  title  = {Classification of left-invariant Einstein metrics on $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ that are bi-invariant under a one-parameter subgroup},
  author = {Vicente Cortés and Jeremias Ehlert and Alexander S. Haupt and David Lindemann},
  journal= {arXiv preprint arXiv:2201.07343},
  year   = {2022}
}

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14 pages

Classification of left-invariant Einstein metrics on $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ that are bi-invariant under a one-parameter subgroup

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Keywords

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