Essential points of conformal vector fields

Abstract

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

Cited by in corpus (3)

• Gravitation in flat spacetime from entanglement
• Zeros of conformal fields in any metric signature
• Two-jets of conformal fields along their zero sets