Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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LEFT INVARIANT LORENTZIAN METRICS AND CURVATURES ON NON-UNIMODULAR LIE GROUPS OF DIMENSION THREE

  • Ku Yong Ha (Department of mathematics Sogang University) ;
  • Jong Bum Lee (Department of mathematics Sogang University)
  • Received : 2022.05.17
  • Accepted : 2022.10.27
  • Published : 2023.01.01
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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 each of these groups. Our study is a continuation and extension of the previous studies done in [3] for Riemannian metrics and in [1] for Lorentzian metrics on unimodular Lie groups.

Keywords

Acknowledgement

The authors would like to thank Professor Kyung Bai Lee for thorough reading and valuable comments in their original version. These comments made our exposition much more transparent than before.

References

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