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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Positive scalar curvature and odd order
abelian fundamental groups


Author: Reinhard Schultz
Journal: Proc. Amer. Math. Soc. 125 (1997), 907-915
MSC (1991): Primary 53C21, 55N15, 57R75; Secondary 53C20, 57R85
MathSciNet review: 1363184
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Abstract: If a smooth manifold has a Riemannian metric with positive scalar curvature, it follows immediately that the universal covering also has such a metric. The paper establishes a converse if the manifold in question is closed of dimension at least 5 and the fundamental group is an elementary abelian $p$-group of rank 2, where $p$ is an odd prime.


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Additional Information

Reinhard Schultz
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Address at time of publication: Department of Mathematics, University of California, Riverside, California 92521
Email: schultz@math.ucr.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03683-6
PII: S 0002-9939(97)03683-6
Received by editor(s): February 13, 1995
Received by editor(s) in revised form: September 13, 1995
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1997 American Mathematical Society