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arXiv · 0905.0262

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

Volodymyr Kiosak·Vladimir S. Matveev
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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.

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Volodymyr Kiosak, Vladimir S. Matveev. 2009-07-16. There are no conformal Einstein rescalings of complete pseudo-Riemannian Einstein metrics. https://doi.org/10.1016/j.crma.2009.06.017

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