  In this article we make a thorough classification of (not necessarily
complete) $n$-dimensional vacuum static spaces $(M,g,f)$ with harmonic
curvature and, as a corollary, obtain a classification of complete vacuum
static spaces with harmonic curvature. Indeed, we showed that $(M,g,f)$ is
locally isometric to one of the following four types; (i) the Riemannian
product of an Einstein manifold and a vacuum static space, (ii) the warped
product over an interval with an Einstein manifold as fiber, (iii) an Einstein
manifold, (iv) the Riemannian product of two Einstein manifolds.

Differential Geometry