The conformal Killing equation on forms -- prolongations and applications

Details The conformal Killing equation on forms -- prolongations and applications The conformal Killing equation on forms -- prolongations and applications

2006-01-31

arxiv.org/abs/math/0601751v1

Differ.Geom.Appl.26:244-266,2008

Mathematics

Differential Geometry

37 pages

Scientific paper

10.1016/j.difgeo.2007.11.014

We construct a conformally invariant vector bundle connection such that its equation of parallel transport is a first order system that gives a prolongation of the conformal Killing equation on differential forms. Parallel sections of this connection are related bijectively to solutions of the conformal Killing equation. We construct other conformally invariant connections, also giving prolongations of the conformal Killing equation, that bijectively relate solutions of the conformal Killing equation on $k$-forms to a twisting of the conformal Killing equation on (k - l)-forms for various integers l. These tools are used to develop a helicity raising and lowering construction in the general setting and on conformally Einstein manifolds.

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