Ternary invariant differential operators acting on spaces of weighted densities

We classify ternary differential operators over $n$-dimensional manifolds. These operators act on the spaces of weighted densities and are invariant with respect to the Lie algebra of vector fields. For $n=1$, some of these operators can be expressed in terms of the de Rham exterior differential, the Poisson bracket, the Grozman operator, and the Feigin–Fuchs antisymmetric operators; four of the operators are new up to dualizations and permutations. For $n>1$, we list multidimensional conformal tranvectors, i.e., operators acting on the spaces of weighted densities and invariant with respect to $\mathfrak o(p+1,q+1)$, where $p+q=n$. With the exception of the scalar operator, these conformally invariant operators are not invariant with respect to the whole Lie algebra of vector fields.