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ON THE TOPOLOGY OF SCALAR-FLAT MANIFOLDS

Published online by Cambridge University Press:  09 April 2001

ANAND DESSAI
ANAND DESSAI
Affiliation:
Department of Mathematics, University of Augsburg, D-86135 Augsburg, Germany; e-mail: [email protected]
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Abstract

Let M be a simply connected closed manifold of dimension greater than 4 which does not admit a metric with positive scalar curvature. We give necessary conditions for M to admit a scalar-flat metric. These conditions involve the first Pontrjagin class and the cohomology ring of M. As a consequence, any simply connected scalar-flat manifold of dimension greater than 4 with vanishing first Pontrjagin class admits a metric with positive scalar curvature. We also describe some relations between scalar-flat metrics, almost complex structures and the free loop space.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 2 , March 2001 , pp. 203 - 209
Copyright
© The London Mathematical Society 2001

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