On symmetric CR geometries of hypersurface type
Complex Variables
2018-08-10 v3 Differential Geometry
Abstract
We study non-degenerate CR geometries of hypersurface type that are symmetric in the sense that, at each point, there is a CR transformation reversing the CR distribution at that point. We show that such geometries are either flat or homogeneous. We show that non-flat non-degenerate symmetric CR geometries of hypersurface type are covered by CR geometries with a compatible pseudo-Riemannian metric preserved by all symmetries. We construct examples of simply connected flat non-degenerate symmetric CR geometries of hypersurface type that do not carry a pseudo-Riemannian metric compatible with the symmetries.
Cite
@article{arxiv.1707.07531,
title = {On symmetric CR geometries of hypersurface type},
author = {Jan Gregorovič and Lenka Zalabová},
journal= {arXiv preprint arXiv:1707.07531},
year = {2018}
}
Comments
21 pp, major revision, Sections 4.3, 4.4, 6.2 added