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Vacuum Static Spaces With Harmonic Curvature

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  • Jongsu Kim

Abstract

In this paper, we make a thorough classification of (not necessarily complete) n$n$‐dimensional vacuum static spaces (M,g,f)$(M,g,f)$ 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)$(M,g,f)$ 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, and (iv) the Riemannian product of two Einstein manifolds.

Suggested Citation

  • Jongsu Kim, 2026. "Vacuum Static Spaces With Harmonic Curvature," Mathematische Nachrichten, Wiley Blackwell, vol. 299(5), pages 1249-1263, May.
    • Handle: RePEc:bla:mathna:v:299:y:2026:i:5:p:1249-1263
    DOI: 10.1002/mana.70138
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