Special metrics and scales in parabolic geometry

• 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

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.

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