Critical metrics of the Schouten functional.

Given a Riemannian metric on a compact smooth manifold, we consider its Schouten tensor, which is a tensor field of type (0, 2) arising in the remainder of the Weyl part in the standard decomposition of the curvature tensor of the metric. We study extremal properties of the Schouten functional, defined to be the scaling-invariant L-norm of the Schouten tensor. It is proved, for instance, that space form metrics are characterized as critical points of the Schouten functional among conformally flat metrics. [ABSTRACT FROM AUTHOR]