Mathematical Research Letters

Volume 3 (1996)

Number 2

Four-Manifolds without Einstein Metrics

Pages: 133 – 147



Claude LeBrun (State University of New York)


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.

Published 1 January 1996