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	https://arxiv.org/pdf/2002.02199.pdf https://link.springer.com/article/10.1007/s10455-022-09866-w
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.
Related projects:	Invariantní diferenciální operátory a jejich aplikace v geometrickém modelování a v teorii optimálního řízení Symetrie a invariance v analýze, geometrickém modelování a teorii optimálního řízení