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arXiv · hep-th/0109210

A conformally invariant differential operator on Weyl tensor densities

Thomas Branson·A. Rod Gover
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Abstract

We derive a tensorial formula for a fourth-order conformally invariant differential operator on conformal 4-manifolds. This operator is applied to algebraic Weyl tensor densities of a certain conformal weight, and takes its values in algebraic Weyl tensor densities of another weight. For oriented manifolds, this operator reverses duality: For example in the Riemannian case, it takes self-dual to anti-self-dual tensors and vice versa. We also examine the place that this operator occupies in known results on the classification of conformally invariant operators, and we examine some related operators.

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Thomas Branson, A. Rod Gover. 2001-09-27. A conformally invariant differential operator on Weyl tensor densities. https://doi.org/10.1016/s0393-0440(01)00086-9

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