English

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

R2 v1 2026-06-21T16:11:06.171Z