SOME UNSTABLE CRITICAL METRICS FOR THE L-n/2-NORM OF THE CURVATURE TENSOR

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M given by R-n/2(g) := integral(M) vertical bar R(g)vertical bar(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.