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

摘要

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 some results in [28] and extends the results of [10,28], solving a problem posed by Lie (1882) [21]. (C) 2020 Elsevier Masson SAS. All rights reserved.