Some constructions of formally self-adjoint conformally covariant polydifferential operators

We introduce the notion of formally self-adjoint conformally covariant polydifferential operators and give some constructions families such operators. In one direction, we show that any homogeneous variational scalar Riemannian invariant (CVI) induces these another use ambient metric to alternative certain produced this way, which is a self-adjoint, fourth-order, tridifferential operator should be regarded as simplest fully nonlinear analogue Paneitz operator.