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arXiv · 2209.02208

Left invariant Lorentzian metrics and curvatures on non-unimodular Lie groups of dimension three

Ku Yong Ha·Jong Bum Lee
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Abstract

For each connected and simply connected three-dimensional non-unimodular Lie group, we classify the left invariant Lorentzian metrics up to automorphism, and study the extent to which curvature can be altered by a change of metric. Thereby we obtain the Ricci operator, the scalar curvature, and the sectional curvatures as functions of left invariant Lorentzian metrics on the three-dimensional non-unimodular Lie groups. Our study is a continuation and extension of the previous studies done in \cite{HL2009_MN} for Riemannian metrics on three-dimensional Lie groups and in \cite{BC} for Lorentzian metrics on three-dimensional unimodular Lie groups.

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Ku Yong Ha, Jong Bum Lee. 2022-09-06. Left invariant Lorentzian metrics and curvatures on non-unimodular Lie groups of dimension three. https://arxiv.org/abs/2209.02208

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