There are no conformal Einstein rescalings of complete pseudo-Riemannian Einstein metrics

Abstract

We prove the following statement: Let g be a light-line-complete pseudo-Riemannian Einstein metric of indefinite signature on a connected (n>2)-dimensional manifold M. Assume that a conformally equivalent metric is also Einstein. Then, the metrics are proportional with a constant coefficient. If in addition the manifold is closed, the assumption that the manifold is light-line-complete could be omitted.

3 pages, no figures

References in corpus (1)

• Twistor spinors with zero on Lorentzian 5-space

Cited by in corpus (3)

• Proof of projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two
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