Abstract
A rigidity result of the complete n-dimensional spin Ricci flat manifolds admitting a certain smooth S1 action is proved, provided that the action has fixed points and the metric is asymptotically flat. Such manifolds are isometric to the n-dimensional Riemannian Schwarzschild metric.
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Hwang, S. A Rigidity Theorem for Ricci Flat Metrics. Geometriae Dedicata 71, 5–17 (1998). https://doi.org/10.1023/A:1005094911005
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DOI: https://doi.org/10.1023/A:1005094911005