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arXiv · 2308.15924

Vacuum static spaces with harmonic curvature

Jongsu Kim
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Abstract

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.

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Jongsu Kim. 2023-08-30. Vacuum static spaces with harmonic curvature. https://arxiv.org/abs/2308.15924

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