On The Stability of The L^p Norm of The Curvature Tensor

Abstract

We investigate stability and local minimizing properties of the Riemannian functional defined by the L^p norm of the curvature tensor on the space of Riemannian metrics on a closed manifold. Riemannian metrics with constant curvature and products of such metrics are critical points of this functional. We prove that these points are strictly stable for this functional and if (M; g) is a manifold of this type, g has a neighborhood U such that g is the strict minima on it.