English

Essential points of conformal vector fields

Differential Geometry 2019-01-08 v4

Abstract

For a conformal vector field ξ\xi on a Riemannian manifold, we say that a point is essential if there is no local metric in the conformal class for which ξ\xi is Killing. We show that the only essential points are isolated zeros of ξ\xi. As an application, we show that every connected component of the zero set of ξ\xi is totally umbilical.

Keywords

Cite

@article{arxiv.1002.0482,
  title  = {Essential points of conformal vector fields},
  author = {Florin Belgun and Andrei Moroianu and Liviu Ornea},
  journal= {arXiv preprint arXiv:1002.0482},
  year   = {2019}
}
R2 v1 2026-06-21T14:42:25.155Z