  We consider the Riemannian functional defined on the space of Riemannian
metrics with unit volume on a closed smooth manifold $M$ given by
$\mathcal{R}_{\frac{n}{2}}(g):= \int_M |R(g)|^{\frac{n}{2}}dv_g$ where $R(g)$,
$dv_g$ denote the Riemannian curvature and volume form corresponding to $g$. We
show that there are locally symmetric spaces which are unstable critical points
for this functional.
