Invariant Prolongation of BGG-operators in Conformal Geometry

Matthias Hammerl

Address: Institut für Mathematik, Universität Wien Nordbergstraße 15, A–1090 Wien, Austria


Abstract: BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and conformal Killing tensors. We present a deformation procedure of the tractor connection which yields an invariant prolongation of the first operator. The explicit calculation is presented in the case of conformal Killing forms.

AMSclassification: primary 53A30; secondary 35N10, 35C15, 58J70.

Keywords: conformal geometry, invariant differential operators, overdetermined systems, prolongation, tractor calculus.