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

 

Remark about scalar curvature and Riemannian submersions


Author: John Lott
Journal: Proc. Amer. Math. Soc. 135 (2007), 3375-3381
MSC (2000): Primary 53C21; Secondary 58G25
Published electronically: June 20, 2007
MathSciNet review: 2322770
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider modified scalar curvature functions for Riemannian manifolds equipped with smooth measures. Given a Riemannian submersion whose fiber transport is measure-preserving up to constants, we show that the modified scalar curvature of the base is bounded below in terms of the scalar curvatures of the total space and fibers. We give an application concerning scalar curvatures of smooth limit spaces arising in bounded curvature collapses.


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Additional Information

John Lott
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043
Email: lott@umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08852-1
PII: S 0002-9939(07)08852-1
Received by editor(s): May 10, 2005
Received by editor(s) in revised form: July 3, 2006
Published electronically: June 20, 2007
Additional Notes: Research supported by NSF grant DMS-0306242 and the Miller Institute
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.