Some Remarks on the Total CR $Q$ and $Q^{\mathrm{\prime }}$-Curvatures

We prove that the total CR $Q$-curvature vanishes for any compact strictly pseudoconvex CR manifold. We also prove the formal self-adjointness of the $P^{\mathrm{\prime }}$-operator and the CR invariance of the total $Q^{\mathrm{\prime }}$-curvature for any pseudo-Einstein manifold without the assumption that it bounds a Stein manifold.