Displaying similar documents to “Conformal structures associated to generic rank 2 distributions on 5-manifolds -- characterization and Killing-field decomposition.”

Invariant prolongation of BGG-operators in conformal geometry

Matthias Hammerl (2008)

Archivum Mathematicum

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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.

On conformal powers of the Dirac operator on spin manifolds

Matthias Fischmann (2014)

Archivum Mathematicum

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The well known conformal covariance of the Dirac operator acting on spinor fields does not extend to its powers in general. For odd powers of the Dirac operator we derive an algorithmic construction in terms of associated tractor bundles computing correction terms in order to achieve conformal covariance. These operators turn out to be formally (anti-) self-adjoint. Working out this algorithm we recover explicit formula for the conformal third and present a conformal fifth power of the...