Mathematical Research Letters

Volume 4 (1997)

Number 6

On the scalar curvature of Einstein manifolds

Pages: 843 – 854



Fabrizio Catanese (University of Göttingen)

Claude LeBrun (SUNY Stony Brook)


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 \cite[p. 19]{bes}. The proof hinges on showing that the Barlow surface has small deformations with ample canonical line bundle.

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