Sophus Lie 一个问题的解：容许两个射影向量场的 2 维度量的规范型
微分几何
2011-08-08 v2 偏微分方程分析
摘要
我们给出了容许传递保测地线变换 Lie 伪群的 2 维度量的完整规范型列表，并证明了这些规范型互不等距。这解决了由 Sophus Lie 提出的一个问题。
引用
@article{arxiv.0705.3592,
title = {A solution of a problem of Sophus Lie: Normal forms of 2-dim metrics admitting two projective vector fields},
author = {Robert L. Bryant and Gianni Manno and Vladimir S. Matveev},
journal= {arXiv preprint arXiv:0705.3592},
year = {2011}
}
备注
This is an extended version of the paper that will appear in Math. Annalen. Some typos were corrected, references were updated, title was changed (as in the journal version). 31 pages