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

 

Homology vanishing theorems for submanifolds


Author: Theodoros Vlachos
Journal: Proc. Amer. Math. Soc. 135 (2007), 2607-2617
MSC (2000): Primary 53C40; Secondary 53C20.
Published electronically: March 30, 2007
MathSciNet review: 2302582
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Abstract: We relate intrinsic and extrinsic curvature invariants to the homology groups of submanifolds in space forms of nonnegative curvature. More precisely, we provide bounds for the squared length of the second fundamental form, or the Ricci curvature in terms of the mean curvature, which force homology to vanish in a range of intermediate dimensions. Moreover, we give examples which show that these conditions are sharp.


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Additional Information

Theodoros Vlachos
Affiliation: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
Email: tvlachos@uoi.gr

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08901-0
PII: S 0002-9939(07)08901-0
Keywords: Ricci curvature, length of the second fundamental form, mean curvature, homology groups
Received by editor(s): May 9, 2006
Published electronically: March 30, 2007
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.