Schmalz, Gerd

Ganji, Masoud

2019-04

We introduce a CR-invariant class of Lorentzian metrics on a circle bundle over a three-dimensional CR structure, which we call FRT metrics. These metrics generalise the Fefferman metric, allowing for more control of the Ricci curvature, but are more special than the shearfree Lorentzian metrics introduced by Robinson and Trautman. Our main result is a criterion for embeddability of three-dimensional CR structures in terms of the Ricci curvature of the FRT metrics in the spirit of the results by Lewandowski et al. (Class Quantum Gravity 7(11):L241–L246, 1990) and also Hill et al. (Indiana Univ Math J 57(7):3131–3176, 2008. https://doi.org/10.1512/iumj.2008.57.3473).

Annali di Matematica Pura ed Applicata, 198(2), p. 491-503

1618-1891

0373-3114

https://hdl.handle.net/1959.11/27121

Springer

A criterion for local embeddability of three-dimensional CR structures

Journal Article

Publication