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4-Manifolds without Einstein Metrics

Claude LeBrun
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Abstract

It is shown that there are infinitely many compact orientable smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question arise as non-minimal complex algebraic surfaces of general type, and the method of proof stems from Seiberg-Witten theory.

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Claude LeBrun. 1995-11-29. 4-Manifolds without Einstein Metrics. https://arxiv.org/abs/dg-ga/9511015

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