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 which are CR-embedded in 5-dimensional real hyperquadrics in order to classify up to CR symmetries of given by the action of one of the Lie groups or . In the latter case, the CR structure of 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 .
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