Mathematical Research Letters

Volume 3, Issue 2, March 1996 pp. 133-147.

Four-Manifolds without Einstein Metrics

Authors: Claude LeBrun
Author institution: State University of New York

Summary: It is shown that there are infinitely many compact simply connected 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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