洛伦兹李群的齐性测地线（英文）

On Homogeneous Geodesics of Lorentzian Lie Groups

主要讨论了李群的上的左不变洛伦兹度量上的齐性测地线问题.给出了不超过4维的李群上,左不变的平坦的洛伦兹度量的且度量限制在中心上是退化的情况的齐性测地线问题的分类.表明了存在只有一个空的齐性测地线的李群.

The homogeneous geodesics of some Lie groups with left invariant Lorentz metrics are studied. Up to dimension four, the homogeneous geodesics of left invariant Lorentzian flat metrics on Lie groups whose restriction of metrics on centers are degenerate are obtained. It shows that there exist some Lie groups with invariant Lorentzian metrics which admit only one null homogeneous geodesic.