Conformally invariant wave equation for a symmetric second rank tensor (spin-2) in d-dimensional curved background

We build the general conformally invariant linear wave operator for a free, symmetric, second-rank tensor field in a d-dimensional ($dgeqslant 2$) metric manifold, and explicit the special case of maximally symmetric spaces. Under the assumptions made, this conformally invariant wave operator is unique. The corresponding conformally invariant wave equation can be obtained from a Lagrangian which is explicitly given. We discuss how our result compares to previous works, in particular we hope to clarify the situation between conflicting results.