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

 

Nonpositivity: Curvature vs. curvature operator


Authors: C. S. Aravinda and F. T. Farrell
Journal: Proc. Amer. Math. Soc. 133 (2005), 191-192
MSC (2000): Primary 32Q05, 53C20
Published electronically: June 2, 2004
MathSciNet review: 2085169
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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.


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Additional 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
Email: farrell@math.binghamton.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07531-8
PII: S 0002-9939(04)07531-8
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
Article copyright: © Copyright 2004 American Mathematical Society