容许恰好一个射影向量场的二维度量
微分几何
2009-10-21 v2 偏微分方程分析
摘要
我们给出了容许本质射影向量场的所有二维度量的完整列表。这解决了 Sophus Lie 于 1882 年明确提出的问题。
引用
@article{arxiv.0802.2344,
title = {Two-dimensional metrics admitting precisely one projective vector field},
author = {Vladimir S. Matveev},
journal= {arXiv preprint arXiv:0802.2344},
year = {2009}
}
备注
42 pages, no figures. The changes w.r.t. (v1) are the following: A paragraph with explanations was added in the introduction, the title was changed, misprints were corrected, references were updated, appendix (by A. Bolsinov, V. Matveev and G. Pucacco) is now incorporated in the paper (it was separately posted as arXiv:0802.2346v1). The paper is accepted to Math. Ann