Two-jets of conformal fields along their zero sets (Q1935627)

This report studies zero sets of a conformal vector field on a pseudo-Riemannian manifold of dimension three or above. The connected components of the zero-set of such a conformal vector field are of two types, the so-called essential, and respectively, non-essential type. The author presents some original results regarding the conformal-equivalence type of the 2-jet of the conformal vector field. The report will be of interest to many mathematicians who do research on pseudo-Riemannian manifolds.