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

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Kiosak, Volodymyr
Matveev, Vladimir S.
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Abstract
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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.
Comment: 3 pages, no figures
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Mathematics - Differential Geometry, Mathematical Physics, 53A30, 53C25, 53C22, 53C50, 53C21
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