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Smooth structures and Einstein metrics on

Published online by Cambridge University Press:  01 September 2009

RAREŞ RǍSDEACONU  and
IOANA ŞUVAINA
RAREŞ RǍSDEACONU
Affiliation:
Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, 91904, Israel. e-mail: [email protected]
IOANA ŞUVAINA
Affiliation:
Courant Institute of Mathematical Sciences, NYU, 251 Mercer St., New York, NY 10012, U.S.A. e-mail: [email protected]
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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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