Normal forms of two-dimensional metrics admitting exactly one essential projective vector field
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.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.