Einstein metrics and smooth structures

We prove that there are infinitely many pairs of homeomorphic non-diffeomorphic smooth 4–manifolds, such that in each pair one manifold admits an Einstein metric and the other does not. We also show that there are closed 4–manifolds with two smooth structures which admit Einstein metrics with opposite signs of the scalar curvature.

Keywords

Einstein metric, smooth structure, 4–manifold

Mathematical Subject Classification

Primary: 57R55, 57R57, 53C25

Secondary: 14J29

References

Forward citations

Publication

Received: 8 September 1997

Revised: 14 January 1998

Accepted: 15 January 1998

Published: 16 January 1998

Proposed: Peter Kronheimer

Seconded: Ronald Stern, Gang Tian

Authors

Dieter Kotschick
Mathematisches Institut Universität Basel Rheinsprung 21 4051 Basel Switzerland

Volume 2, issue 1 (1998)

Dieter Kotschick