Two-dimensional metrics admitting precisely one projective vector field

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.

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