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

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

2009-05-03

arxiv.org/abs/0905.0262v2

C. R. Acad. Sci. Paris, Ser. I 347(2009) 1067--1069

Mathematics

Differential Geometry

3 pages, no figures

Scientific paper

10.1016/j.crma.2009.06.017

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.

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