3-folds CR-embedded in 5-dimensional real hyperquadrics

Curtis Porter

doi:10.1016/j.geomphys.2021.104107

paper

3-folds CR-embedded in 5-dimensional real hyperquadrics

arXiv:1808.08625 · doi:10.1016/j.geomphys.2021.104107

Abstract

E. Cartan's method of moving frames is applied to 3-dimensional manifolds $M$ which are CR-embedded in 5-dimensional real hyperquadrics $Q$ in order to classify $M$ up to CR symmetries of $Q$ given by the action of one of the Lie groups $S U (3, 1)$ or $S U (2, 2)$ . In the latter case, the CR structure of $M$ derives from a shear-free null geodesic congruence on Minkowski spacetime, and the relationship to relativity is discussed. In both cases, we compute which homogeneous CR 3-folds appear in $Q$ .

Substantial revision of Levi-nondegenerate classification, both intrinsic and extrinsic, for clarity; Levi-flat case now included; 32 pages