Let $M$ be a smooth, closed manifold of dimension $n>2$. Let $L_g$ be the conformal Laplacian of the metric $g$. That is, $L_g=\Delta_g + \frac{n2}{4(n1)}R_g$, where $R_g$ is the scalar curvature of the metric $g$. Is the set of $C^2$ Riemannian metrics on $M$ such that conformal Laplacian has a trivial kernel dense with respect to the $C^2$ norm?
