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http://dx.doi.org/10.4134/JKMS.j210460

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)
Publication Information
Journal of the Korean Mathematical Society / v.59, no.4, 2022 , pp. 651-684 More about this Journal
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.
Keywords
Moduli space of left-invariant metrics; Lorentzian metrics; 3-dimensional Lie groups; generalized Ricci solitons;
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