Flat Left-Invariant Lorentzian Metrics on Almost Abelian Lie Groups

Key Points

• 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.