English

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

Differential Geometry 2021-02-23 v3

Abstract

E. Cartan's method of moving frames is applied to 3-dimensional manifolds MM which are CR-embedded in 5-dimensional real hyperquadrics QQ in order to classify MM up to CR symmetries of QQ given by the action of one of the Lie groups SU(3,1)SU(3,1) or SU(2,2)SU(2,2). In the latter case, the CR structure of MM 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 QQ.

Keywords

Cite

@article{arxiv.1808.08625,
  title  = {3-folds CR-embedded in 5-dimensional real hyperquadrics},
  author = {Curtis Porter},
  journal= {arXiv preprint arXiv:1808.08625},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-23T03:44:15.736Z