Journal of the
Korean Mathematical Society JKMS

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: Non-unimodular three dimensional Lie groups, left invariant Lorentzian metrics, Ricci operators

MSC numbers: Primary 53C50; Secondary 22E15

Supported by: The authors were partially supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, NRF-2021R1I1A1A01054732 and NRF-2016R1D1A1B01006971, respectively.