Conformal diffeomorphisms preserving the Ricci tensor

Kühnel, W.; Rademacher, H.-B.

doi:10.1090/S0002-9939-1995-1260173-6

Conformal diffeomorphisms preserving the Ricci tensor
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by W. Kühnel and H.-B. Rademacher PDF

Proc. Amer. Math. Soc. 123 (1995), 2841-2848 Request permission

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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