Note on pre-Courant algebroid structures for parabolic geometries

Details Note on pre-Courant algebroid structures for parabolic geometries Note on pre-Courant algebroid structures for parabolic geometries

2007-09-06

arxiv.org/abs/0709.0919v3

Mathematics

Differential Geometry

A short note on Courant brackets on parabolic geometries. 2nd Version. Removed an erronous proof

Scientific paper

This note aims to demonstrate that every parabolic geometry has a naturally
defined per-Courant algebro\"id structure. This structure is a Courant
algebro\"id if and only if the the curvature $\kappa$ 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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