Vacuum Static Spaces with Positive Isotropic Curvature

In this paper, we study vacuum static spaces with positive isotropic curvature. We prove that if $(M^n, g, f)$, $n ge 4$, is a compact vacuum static space with positive isotropic curvature, then up to finite cover, $M$ is isometric to a sphere ${Bbb S}^n$ or the product of a circle ${Bbb S}^1$ with an $(n-1)$-dimensional sphere ${Bbb S}^{n-1}$.