论文标题
左lorentzian指标和曲率在非较小的谎言群体上
Left invariant Lorentzian metrics and curvatures on non-unimodular Lie groups of dimension three
论文作者
论文摘要
对于每个连接并简单地连接的三维非潜在谎言组，我们将左不变的洛伦兹指标分类为自动形态，并研究可以通过度量的变化来改变曲率的程度。因此，我们获得了RICCI操作员，标量曲率和截面曲率，作为在三维非微分谎言基团上左不变的Lorentzian指标的函数。 我们的研究是针对三维谎言组的Riemannian指标在\ cite {hl2009_mn}中进行的先前研究的延续和扩展，以及三维指标的三维指标的三维指标。
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 the three-dimensional non-unimodular Lie groups. Our study is a continuation and extension of the previous studies done in \cite{HL2009_MN} for Riemannian metrics on three-dimensional Lie groups and in \cite{BC} for Lorentzian metrics on three-dimensional unimodular Lie groups.
