On the Scalar Curvature of Einstein Manifolds

Details On the Scalar Curvature of Einstein Manifolds On the Scalar Curvature of Einstein Manifolds

1997-05-14

arxiv.org/abs/dg-ga/9705007v1

Mathematics

Algebraic Geometry

LaTeX. 14 pages

Scientific paper

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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