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

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

Annals of Global Analysis and Geometry（2023）

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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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Key words

Special linear group,Einstein manifolds,Non-compact homogeneous pseudo-Riemannian manifolds

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