There are no conformal Einstein rescalings of complete pseudo-Riemannian Einstein metrics
Differential Geometry
2011-08-08 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.0905.0262,
title = {There are no conformal Einstein rescalings of complete pseudo-Riemannian Einstein metrics},
author = {Volodymyr Kiosak and Vladimir S. Matveev},
journal= {arXiv preprint arXiv:0905.0262},
year = {2011}
}
Comments
3 pages, no figures