On Symmetric CR Geometries of Hypersurface Type

GREGOROVIC, Jan and Lenka ZALABOVÁ. On Symmetric CR Geometries of Hypersurface Type. JOURNAL OF GEOMETRIC ANALYSIS. NEW YORK: SPRINGER, 2019, vol. 29, No 4, p. 3135-3159. ISSN 1050-6926. Available from: https://dx.doi.org/10.1007/s12220-018-00110-1.

Basic information

• Original name: On Symmetric CR Geometries of Hypersurface Type
• Authors: GREGOROVIC, Jan (guarantor) and Lenka ZALABOVÁ (203 Czech Republic, belonging to the institution).
• Edition: JOURNAL OF GEOMETRIC ANALYSIS, NEW YORK, SPRINGER, 2019, 1050-6926.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 0.924
• RIV identification code: RIV/00216224:14310/19:00108221
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1007/s12220-018-00110-1
• UT WoS: 000488929600007
• Keywords in English: CR geometry; Homogeneous manifold; Webster metric
• Tags: rivok

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.

Links

• GA17-01171S, research and development project: Name: Invariantní diferenciální operátory a jejich aplikace v geometrickém modelování a v teorii optimálního řízení

Investor: Czech Science Foundation