2023/08/30 by Kim, Jongsu
#53C21 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2308.15924
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.