On symmetric CR geometries of hypersurface type

Jan Gregorovič; Lenka Zalabová

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arXiv · 1707.07531

On symmetric CR geometries of hypersurface type

Jan Gregorovič·Lenka Zalabová

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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.

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Jan Gregorovič, Lenka Zalabová. 2017-07-24. On symmetric CR geometries of hypersurface type. https://arxiv.org/abs/1707.07531

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