Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE MODULI SPACES OF LORENTZIAN LEFT-INVARIANT METRICS ON THREE-DIMENSIONAL UNIMODULAR SIMPLY CONNECTED LIE GROUPS

  • Boucetta, Mohamed (Department of Mathematics University Cadi Ayyad Faculty of Sciences and Techniques Marrakech) ;
  • Chakkar, Abdelmounaim (Department of Mathematics University Cadi Ayyad Faculty of Sciences and Techniques Marrakech)
  • Received : 2021.07.26
  • Accepted : 2022.04.25
  • Published : 2022.07.01
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Abstract

Let G be an arbitrary, connected, simply connected and unimodular Lie group of dimension 3. On the space 𝔐(G) of left-invariant Lorentzian metrics on G, there exists a natural action of the group Aut(G) of automorphisms of G, so it yields an equivalence relation ≃ on 𝔐(G), in the following way: h1 ≃ h2 ⇔ h2 = 𝜙*(h1) for some 𝜙 ∈ Aut(G). In this paper a procedure to compute the orbit space Aut(G)/𝔐(G) (so called moduli space of 𝔐(G)) is given.

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Acknowledgement

We thank the anonymous referees for their careful reading of the paper and very helpful comments.

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