Vacuum Static Spaces With Harmonic Curvature

초록

In this paper, we make a thorough classification of (not necessarily complete) -dimensional vacuum static spaces with harmonic curvature and, as a corollary, obtain a classification of complete vacuum static spaces with harmonic curvature. Indeed, we showed that 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, and (iv) the Riemannian product of two Einstein manifolds.

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