Special metrics and scales in parabolic geometry
Differential Geometry
2022-06-07 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2002.02199,
title = {Special metrics and scales in parabolic geometry},
author = {Michael Eastwood and Lenka Zalabová},
journal= {arXiv preprint arXiv:2002.02199},
year = {2022}
}
Comments
We have made several modifications, especially in linking our results to the literature on CR geometry. 30 pages