Left invariant Lorentzian metrics and curvatures on non-unimodular Lie groups of dimension three
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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 each of these groups. Our study is a continuation and extension of the previous studies done in \cite{HL2009_MN} for Riemannian metrics and in \cite{BC} for Lorentzian metrics on unimodular Lie groups.
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 each of these groups. Our study is a continuation and extension of the previous studies done in \cite{HL2009_MN} for Riemannian metrics and in \cite{BC} for Lorentzian metrics on unimodular Lie groups.
참고문헌 (8)
- Mohamed Boucetta, "The moduli spaces of Lorentzian left-invariant metrics on three-dimensional unimodular simply connected Lie groups", 대한수학회지, 59(4), pp.651~684 (2022), 대한수학회[DOI]
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- 하구용, "Left invariant Lorentzian metrics and curvatures on non-unimodular Lie groups of dimension three", 대한수학회지, 60(1), pp.143~165 (2023), 대한수학회[DOI]
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