Coupling solutions of BGG-equations in conformal spin geometry

2010/09/08 by Matthias Hammerl, Hammerl, Matthias
Mathematics · #35N10 #53A30 #53B15 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:35N10 #msc:53A30 #msc:53B15

paper · pdf · doi:10.48550/arxiv.1009.1547

14 pages

arxiv created 2010/09/08 · arxiv updated 2010/09/09

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.

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