Mathematical Research Letters

Volume 4, Issue 6, November 1997 pp. 843-854.

On the scalar curvature of Einstein manifolds

Authors: Fabrizio Catanese (1) and Claude LeBrun (2)
Author institution: University of Göttingen (1) SUNY Stony Brook (2)

Summary: 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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