On the Scalar Curvature of Einstein Manifolds
Fabrizio Catanese, Claude LeBrun
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.
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