Coupling solutions of BGG-equations in conformal spin geometry

Details Coupling solutions of BGG-equations in conformal spin geometry Coupling solutions of BGG-equations in conformal spin geometry

2010-09-08

arxiv.org/abs/1009.1547v1

Mathematics

Differential Geometry

14 pages

Scientific paper

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.

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