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Smooth structures and Einstein metrics on ![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20151023034000227-0265:S0305004109002527_inline1.gif?pub-status=live)
Published online by Cambridge University Press: 01 September 2009
Abstract
We show that each of the topological 4-manifolds , for k = 5, 6, 7, 8 admits a smooth structure which has an Einstein metric of scalar curvature s > 0, a smooth structure which carries an Einstein metric with s < 0 and infinitely many non-diffeomorphic smooth structures which do not admit Einstein metrics. We also exhibit new examples of higher dimensional manifolds carrying Einstein metrics of both positive and negative scalar curvature.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 2 , September 2009 , pp. 409 - 417
- Copyright
- Copyright © Cambridge Philosophical Society 2009
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