Two-dimensional metrics admitting precisely one projective vector field
Differential Geometry
2009-10-21 v2 Analysis of PDEs
Abstract
We give a complete list of two-dimensional metrics that admit an essential projective vector field. This solves a problem explicitly posed by Sophus Lie in 1882.
Cite
@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}
}
Comments
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