Coupling solutions of BGG-equations in conformal spin geometry
Differential Geometry
2010-09-09 v1
Abstract
BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and sufficient additional integrability conditions on a solution. We then discuss a procedure for coupling known solutions of BGG-equations to produce new ones. Employing a suitable calculus for conformal spin structures this yields explicit coupling formulas and conditions between almost Einstein scales, conformal Killing forms and twistor spinors. Finally we discuss a class of generic twistor spinors that provides an invariant decomposition of conformal Killing fields.
Keywords
Cite
@article{arxiv.1009.1547,
title = {Coupling solutions of BGG-equations in conformal spin geometry},
author = {Matthias Hammerl},
journal= {arXiv preprint arXiv:1009.1547},
year = {2010}
}
Comments
14 pages