  Recently Boulanger and Leclercq have constructed cubic four derivative
$3-3-2$ vertex for interaction of spin 3 and spin 2 particles. This vertex is
trivially invariant under the gauge transformations of spin 2 field, so it
seemed that it could be expressed in terms of (linearized) Riemann tensor. And
indeed in this paper we managed to reproduce this vertex in the form $R
\partial \Phi \partial \Phi$, where $R$ -- linearized Riemann tensor and $\Phi$
-- completely symmetric third rank tensor. Then we consider deformation of this
vertex to $(A)dS$ space and show that such deformation produce "standard"
gravitational interaction for spin 3 particles (in linear approximation) in
agreement with general construction of Fradkin and Vasiliev. Then we turn to
the massive case and show that the same higher derivative terms allows one to
extend gauge invariant description of massive spin 3 particle from constant
curvature spaces to arbitrary gravitational backgrounds satisfying $R_{\mu\nu}
= 0$.
