4-Manifolds without Einstein Metrics

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.

9 pages, latex, with \Bbb font redefined for WWW use

References in corpus (2)

• Algebraic surfaces and Seiberg-Witten invariants
• Polarized 4-Manifolds, Extremal Kähler Metrics, and S-W Theory

Cited by in corpus (2)

• The Spin${}^c$ Dirac Operator on Hypersurfaces and Applications
• Eigenvalue Estimates of the ${\mathrm{spin}}^c$ Dirac Operator and Harmonic Forms on Kähler-Einstein Manifolds