Special metrics and scales in parabolic geometry

Michael Eastwood; Lenka Zalabová

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arXiv · 2002.02199

Special metrics and scales in parabolic geometry

Michael Eastwood·Lenka Zalabová

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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.

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Michael Eastwood, Lenka Zalabová. 2020-02-06. Special metrics and scales in parabolic geometry. https://arxiv.org/abs/2002.02199

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