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arXiv · 1207.4005

Parabolic geodesics as parallel curves in parabolic geometries

Marc Herzlich
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Abstract

We give a simple characterization of the parabolic geodesics introduced by Cap, Slovak and Zadnik for all parabolic geometries. This goes through the definition of a natural connection on the space of Weyl structures. We then show that parabolic geodesics can be characterized as the following data: a curve on the manifold and a Weyl structure along the curve, so that the curve is a geodesic for its companion Weyl structure and the Weyl structure is parallel along the curve and in the direction of the tangent vector of the curve.

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Marc Herzlich. 2012-07-17. Parabolic geodesics as parallel curves in parabolic geometries. https://arxiv.org/abs/1207.4005

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