Essential points of conformal vector fields

Details Essential points of conformal vector fields Essential points of conformal vector fields

2010-02-02

arxiv.org/abs/1002.0482v4

Journal of Geometry and Physics 61, no. 3, 589-593 (2011)

Mathematics

Differential Geometry

Scientific paper

10.1016/j.geomphys.2010.11.007

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.

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