Zeros of conformal fields in any metric signature

Details Zeros of conformal fields in any metric signature Zeros of conformal fields in any metric signature

2010-11-24

arxiv.org/abs/1011.5524v1

Classical and Quantum Gravity, vol. 28 (2011), no. 7, art. 075011, 23 pp

Mathematics

Differential Geometry

26 pages

Scientific paper

10.1088/0264-9381/28/7/075011

The connected components of the zero set of any conformal vector field, in a pseudo-Riemannian manifold of arbitrary signature, are shown to be totally umbilical conifold varieties, that is, smooth submanifolds except possibly for some quadric singularities. The singularities occur only when the metric is indefinite, including the Lorentzian case. This generalizes an analogous result in the Riemannian case, due to Belgun, Moroianu and Ornea (2010).

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