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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Conformal diffeomorphisms preserving the Ricci tensor


Authors: W. Kühnel and H.-B. Rademacher
Journal: Proc. Amer. Math. Soc. 123 (1995), 2841-2848
MSC: Primary 53C20; Secondary 53A30, 53C50, 58G30
MathSciNet review: 1260173
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Abstract: We characterize semi-Riemannian manifolds admitting a global conformal transformation such that the difference of the two Ricci tensors is a constant multiple of the metric. Unless the conformal transformation is homothetic, the only possibilities are standard Riemannian spaces of constant sectional curvature and a particular warped product with a Ricci flat Riemannian manifold.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1260173-6
PII: S 0002-9939(1995)1260173-6
Keywords: Semi-Riemannian manifolds, Ricci tensor, conformal mapping, Hessian
Article copyright: © Copyright 1995 American Mathematical Society