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On Symmetric CR Geometries of Hypersurface Type

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GREGOROVIC Jan ZALABOVÁ Lenka

Rok publikování 2019
Druh Článek v odborném periodiku
Časopis / Zdroj JOURNAL OF GEOMETRIC ANALYSIS
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://link.springer.com/article/10.1007/s12220-018-00110-1#Bib1
Doi http://dx.doi.org/10.1007/s12220-018-00110-1
Klíčová slova CR geometry; Homogeneous manifold; Webster metric
Popis 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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