Vacuum Static Spaces with Positive Isotropic Curvature

Abstract

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 ${\mathbb{S}}^n$ or the product of a circle ${\mathbb{S}}^1$ with an $(n-1)$-dimensional sphere ${\mathbb{S}}^{n-1}$.

16 pages without figures. arXiv admin note: text overlap with arXiv:2103.15482