English

Normal forms of two-dimensional metrics admitting exactly one essential projective vector field

Differential Geometry 2020-02-20 v4 Analysis of PDEs

Abstract

We give a complete list of mutually non-diffeomorphic normal forms for the two-dimensional metrics that admit one essential (i.e., non-homothetic) projective vector field. This revises a result from the literature and extends the results of two papers, by R.L. Bryant & G. Manno & V.S. Matveev (2008) and V.S. Matveev (2012) respectively, solving a problem posed by Sophus Lie in 1882.

Keywords

Cite

@article{arxiv.1705.06630,
  title  = {Normal forms of two-dimensional metrics admitting exactly one essential projective vector field},
  author = {Gianni Manno and Andreas Vollmer},
  journal= {arXiv preprint arXiv:1705.06630},
  year   = {2020}
}

Comments

47 pages, 4 figures

R2 v1 2026-06-22T19:51:27.075Z