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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Nonpositivity: Curvature vs. curvature operator
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by C. S. Aravinda and F. T. Farrell
Proc. Amer. Math. Soc. 133 (2005), 191-192
DOI: https://doi.org/10.1090/S0002-9939-04-07531-8
Published electronically: June 2, 2004
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Abstract:

It is shown that there exist closed Riemannian manifolds $M$ all of whose sectional curvatures are negative, but $M$ does not admit any metric with nonpositive curvature operator.
References
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Bibliographic Information
  • C. S. Aravinda
  • Affiliation: Chennai Mathematical Institute, 92, G. N. Chetty Road, Chennai 600 017, India
  • Email: aravinda@cmi.ac.in
  • F. T. Farrell
  • Affiliation: Department of Mathematics, SUNY at Binghamton, Binghamton, New York 13902-6000
  • MR Author ID: 65305
  • Email: farrell@math.binghamton.edu
  • Received by editor(s): September 18, 2003
  • Published electronically: June 2, 2004
  • Additional Notes: The second author was supported in part by a grant from the National Science Foundation
  • Communicated by: Jon G. Wolfson
  • © Copyright 2004 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 191-192
  • MSC (2000): Primary 32Q05, 53C20
  • DOI: https://doi.org/10.1090/S0002-9939-04-07531-8
  • MathSciNet review: 2085169