2019/03/12 by Mohamed Boucetta, Boucetta, Mohamed, Abdelmounaim Chakkar +1
Mathematics · Physics and Astronomy · #22E15 #53C50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1903.05194
openalex publication_date 2019/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are five unimodular simply connected three dimensional unimodular non\nabelian Lie groups: the nilpotent Lie group \Nil, the special unitary\ngroup \SU(2), the universal covering group\n widetilde\PSL(2,\ℝ) of the special linear group, the\nsolvable Lie group \Sol and the universal covering group\n widetilde\E0(2) of the connected component of the Euclidean\ngroup. For each G among these Lie groups, we give explicitly the list of all\nLorentzian left invariant metrics on G, up to un automorphism of G.\nMoreover, for any Lorentzian left invariant metric in this list we give its\nRicci curvature, scalar curvature, the signature of the Ricci curvature and we\nexhibit some special features of these curvatures. Namely, we give all the\nmetrics with constant curvature, semi-symmetric non locally symmetric metrics\nand the Ricci solitons.\n