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

##### Authors
Kiosak, Volodymyr
Matveev, Vladimir S.
##### Description
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
##### Keywords
Mathematics - Differential Geometry, Mathematical Physics, 53A30, 53C25, 53C22, 53C50, 53C21