Note on pre-Courant algebroid structures for parabolic geometries

Stuart Armstrong

Note on pre-Courant algebroid structures for parabolic geometries

Differential Geometry 2011-03-02 v3 General Mathematics

Authors: Stuart Armstrong

Abstract

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.

Cite

@article{arxiv.0709.0919,
  title  = {Note on pre-Courant algebroid structures for parabolic geometries},
  author = {Stuart Armstrong},
  journal= {arXiv preprint arXiv:0709.0919},
  year   = {2011}
}

Comments

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

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