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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Homology vanishing theorems for submanifolds
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by Theodoros Vlachos PDF
Proc. Amer. Math. Soc. 135 (2007), 2607-2617 Request permission

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
  • MR Author ID: 291296
  • Email: tvlachos@uoi.gr
  • Received by editor(s): May 9, 2006
  • Published electronically: March 30, 2007
  • Communicated by: Jon G. Wolfson
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2607-2617
  • MSC (2000): Primary 53C40; Secondary 53C20
  • DOI: https://doi.org/10.1090/S0002-9939-07-08901-0
  • MathSciNet review: 2302582