A Result of Rigidity for Ricci-Flat Warped Products

A Result of Rigidity for Ricci-Flat Warped Products

In this work we prove a result of rigidity on Ricci-flat semi-Riemannian warped products when the base is locally conformally flat with scalar curvature zero and invariant by the action of the pseudo-orthogonal group. We obtain that in these manifolds the fiber must be 1-dimensional. As an applicati...

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Veröffentlicht in:Boletim da Sociedade Brasileira de Matemática 2023-09, Vol.54 (3), Article 35
Hauptverfasser: Menezes, Ilton, Correia, Paula, Pina, Romildo
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Rigidity
Schwarzschild metric
Theoretical
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Zusammenfassung:In this work we prove a result of rigidity on Ricci-flat semi-Riemannian warped products when the base is locally conformally flat with scalar curvature zero and invariant by the action of the pseudo-orthogonal group. We obtain that in these manifolds the fiber must be 1-dimensional. As an application, every metric with these characteristics is a generalized Schwarzschild metric.
ISSN:1678-7544
1678-7714
DOI:10.1007/s00574-023-00352-w