  Let $(M,g)$ be a noncompact complete $n$-manifold with harmonic curvature and
positive Sobolev constant. Assume that $L_2$ norms of Weyl curvature and
traceless Ricci curvature are finite. We prove that $(M,g)$ is Einstein if $n
\ge 5$ and $L_{n/2}$ norms of Weyl curvature and traceless Ricci curvature are
small enough.

Differential Geometry;General Relativity and Quantum Cosmology