Special metrics and scales in parabolic geometry

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Authors

EASTWOOD Michael ZALABOVÁ Lenka

Year of publication 2022
Type Article in Periodical
Magazine / Source Annals of Global Analysis and Geometry
MU Faculty or unit

Faculty of Science

Citation
Web
Doi http://dx.doi.org/10.1007/s10455-022-09866-w
Keywords Projective differential geometry; Conformal differential geometry; Other special differential geometries
Description Given a parabolic geometry, it is sometimes possible to find special metrics characterised by some invariant conditions. In conformal geometry, for example, one asks for an Einstein metric in the conformal class. Einstein metrics have the special property that their geodesics are distinguished, as unparameterised curves, in the sense of parabolic geometry. This property characterises the Einstein metrics. In this article, we initiate a study of corresponding phenomena for other parabolic geometries, in particular for the hypersurface CR and contact Legendrean cases.
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