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arXiv · 1002.0482

Essential points of conformal vector fields

Florin Belgun·Andrei Moroianu·Liviu Ornea
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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.

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Florin Belgun, Andrei Moroianu, Liviu Ornea. 2010-02-02. Essential points of conformal vector fields. https://doi.org/10.1016/j.geomphys.2010.11.007

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