A conformally invariant differential operator on Weyl tensor densities (Q1603282)

The authors study conformally invariant linear differential operators of order 4 on conformal four-manifolds and derive a tensorial formula for this kind of operator. Such 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. Under this operator, self-dual and anti-self-dual Weyl tensor densities are interchanged, in a way reminiscent of the chirality switch effected by the Dirac operator.