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

 

Compact Einstein warped product spaces with nonpositive scalar curvature


Authors: Dong-Soo Kim and Young Ho Kim
Journal: Proc. Amer. Math. Soc. 131 (2003), 2573-2576
MSC (2000): Primary 53B20, 53C20
Published electronically: February 26, 2003
MathSciNet review: 1974657
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Abstract: We study Einstein warped product spaces. As a result, we prove the following: if $M$ is an Einstein warped product space with nonpositive scalar curvature and compact base, then $M$ is simply a Riemannian product space.


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Additional Information

Dong-Soo Kim
Affiliation: Department of Mathematics, College of Natural Sciences, Chonnam National University, Kwangju, 500-757, Korea
Email: dosokim@chonnam.chonnam.ac.kr

Young Ho Kim
Affiliation: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu, 702-701, Korea
Email: yhkim@knu.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06878-3
PII: S 0002-9939(03)06878-3
Keywords: Einstein space, warped product, Ricci tensor, Hessian tensor, Ricci identity
Received by editor(s): August 14, 2000
Received by editor(s) in revised form: July 10, 2001
Published electronically: February 26, 2003
Additional Notes: This work was supported by the Brain Korea 21.
Dedicated: Dedicated to Professor Bang-yen Chen on the occasion of his sixtieth birthday
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2003 American Mathematical Society