On Symmetric CR Geometries of Hypersurface Type
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | JOURNAL OF GEOMETRIC ANALYSIS |
| MU Faculty or unit | |
| Citation | |
| Web | https://link.springer.com/article/10.1007/s12220-018-00110-1#Bib1 |
| Doi | http://dx.doi.org/10.1007/s12220-018-00110-1 |
| Keywords | CR geometry; Homogeneous manifold; Webster metric |
| Description | 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. |
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