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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 | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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Additional Information

C. S. Aravinda
Affiliation: Chennai Mathematical Institute, 92, G. N. Chetty Road, Chennai 600 017, India

F. T. Farrell
Affiliation: Department of Mathematics, SUNY at Binghamton, Binghamton, New York 13902-6000

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