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August 2, 2026Results in MathematicsOpen Access

Flat Left-Invariant Lorentzian Metrics on Almost Abelian Lie Groups

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This research aims to classify the left-invariant Lorentzian metrics on almost abelian Lie groups that have vanishing curvature.
Analyzed the structure of almost abelian Lie groups and their associated Lie algebras.
Developed a classification framework for left-invariant Lorentzian metrics.
Identified inequivalent flat Lorentzian products for each algebra.
Classified all Lie algebras of almost abelian Lie groups admitting a left-invariant Lorentzian metric.
Identified conditions under which these metrics exhibit vanishing curvature.
Established complete classifications of flat Lorentzian products among identified algebras.

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Research identifies metrics in almost abelian lie groups, classifying flat Lorentzian products and algebras.

Bajo et al. (2026) studied this question.

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