论文标题
某些洛伦兹简单谎言群体的大地测量完整性
Geodesic completeness of some Lorentzian simple Lie groups
论文作者
论文摘要
在本文中，我们调查了一个简单的谎言组$ g $在存在$ g $上的剩余不变的杀死矢量field $ z $时，请在一个简单的谎言组$ g $上进行测量完整性。除其他结果外，还可以证明，如果$ z $是及时的，或者$ g $是强烈的因果关系，而$ z $ lightlike，则指标已完成。然后，我们将在更多详细信息中考虑特殊的复杂Lie Group $ SL_2（\ Mathbb {C}）$，并表明其上存在Lightlike Vector Field $ Z $，这意味着地球上的完整性。我们还考虑了$ sl_2（\ mathbb {c}）$上的间距矢量字段$ z $的存在，并提供了等效条件，以使公制完成。这说明了当$ z $具有间距时的情况的复杂性。
In this paper we investigate geodesic completeness of left-invariant Lorentzian metrics on a simple Lie group $G$ when there exists a left-invariant Killing vector field $Z$ on $G$. Among other results, it is proved that if $Z$ is timelike, or $G$ is strongly causal and $Z$ is lightlike, then the metric is complete. We then consider the special complex Lie group $SL_2(\mathbb{C})$ in more details and show that the existence of a lightlike vector field $Z$ on it, implies geodesic completeness. We also consider the existence of a spacelike vector field $Z$ on $SL_2(\mathbb{C})$ and provide an equivalent condition for the metric to be complete. This illustrates the complexity of the situation when $Z$ is spacelike.
