  We consider the Riemannian functional defined on the space of Riemannian
metrics with unit volume on a closed smooth manifold M given by $R_p(g)
:=\int_M|R(g)|^pdvg$ where $R(g)$, $dv_g$ denote the corresponding Riemannian
curvature, volume form and p is a real number greater than or equal to 2. We
prove that $R_p$ restricted to the space of Kahler metrics attains its local
minima at a metric with constant holomorphic sectional curvature.
