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On the Scalar Curvature of Einstein Manifolds

Fabrizio Catanese·Claude LeBrun
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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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Fabrizio Catanese, Claude LeBrun. 1997-05-14. On the Scalar Curvature of Einstein Manifolds. https://arxiv.org/abs/dg-ga/9705007

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