Classification of left-invariant Einstein metrics on SL(2,ℝ)\timesSL(2,ℝ) that are bi-invariant under a one-parameter subgroup

2022/01/18 by Cortés, Vicente, Ehlert, Jeremias, Haupt, Alexander S. +1
#53C25 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2201.07343

Abstract

We classify all left-invariant pseudo-Riemannian Einstein metrics on SL(2,ℝ)× SL(2,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-Kähler metric.

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