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arXiv · 0709.0919

Note on pre-Courant algebroid structures for parabolic geometries

Stuart Armstrong
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Abstract

This note aims to demonstrate that every parabolic geometry has a naturally defined per-Courant algebroïd structure. This structure is a Courant algebroïd if and only if the the curvature $κ$ of the Cartan connection vanishes. In all other cases, if the parabolic geometry is regular, there does not exist a natural universal expression for a Courant bracket.

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Stuart Armstrong. 2011-03-01. Note on pre-Courant algebroid structures for parabolic geometries. https://arxiv.org/abs/0709.0919

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