论文标题
伪和全体形态Riemannian指标的大地测量完整性
Geodesic completeness of pseudo and holomorphic Riemannian metrics on Lie groups
论文作者
论文摘要
本文致力于对真实且复杂的谎言组的剩余指标的测量完整性。我们首先在全体形态环境中建立Euler-Arnold形式主义。我们研究真实的谎言组$ \ mathrm {sl}（2，\ mathbb {r}）$，并重新侵略了测量完整性的已知表征，此外，介绍了一项详细的研究，我们研究了每个可能的测量方法的最大定义域。我们研究了剩余不变的全体形态指标的复杂测量流的完整性和半完整性，尤其是为Lie组$ \ Mathrm {SL}（2，\ Mathbb {C}）$建立完整的分类。
This paper is devoted to geodesic completeness of left-invariant metrics for real and complex Lie groups. We start by establishing the Euler-Arnold formalism in the holomorphic setting. We study the real Lie group $\mathrm{SL}(2, \mathbb{R})$ and reobtain the known characterization of geodesic completeness and, in addition, present a detailed study where we investigate the maximum domain of definition of every single geodesic for every possible metric. We investigate completeness and semicompleteness of the complex geodesic flow for left-invariant holomorphic metrics and, in particular, establish a full classification for the Lie group $\mathrm{SL}(2, \mathbb{C})$.
