On the Scalar Curvature of Einstein Manifolds
arXiv:dg-ga/9705007
Abstract
We show that there are high-dimensional smooth compact manifolds which admit pairs of Einstein metrics for which the scalar curvatures have opposite signs. These are counter-examples to a conjecture considered by Besse. The proof hinges on showing that the Barlow surface has small deformations with ample canonical line bundle.
LaTeX. 14 pages