LEFT INVARIANT LORENTZIAN METRICS AND CURVATURES ON NON-UNIMODULAR LIE GROUPS OF DIMENSION THREE

초록

For each connected and simply connected three-dimensional non-unimodular Lie group, we classify the left invariant Lorentzian met-rics 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.

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