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<p>Almost abelian Lie groups are those admitting a normal subgroup which is commutative and of codimension one. We determine all Lie algebras of almost abelian Lie groups admitting a left-invariant Lorentzian metric of vanishing curvature. For each of those algebras, we completely classify the set of inequivalent flat Lorentzian products.</p>

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Flat Left-Invariant Lorentzian Metrics on Almost Abelian Lie Groups

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月31日

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  • Ignacio Bajo,
  • Saïd Benayadi,
  • Hicham Lebzioui

摘要

Almost abelian Lie groups are those admitting a normal subgroup which is commutative and of codimension one. We determine all Lie algebras of almost abelian Lie groups admitting a left-invariant Lorentzian metric of vanishing curvature. For each of those algebras, we completely classify the set of inequivalent flat Lorentzian products.