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Nonpositivity: Curvature vs. curvature operator

Author(s): C. S. Aravinda; F. T. Farrell
Journal: Proc. Amer. Math. Soc. 133 (2005), 191-192.
MSC (2000): Primary 32Q05, 53C20
Posted: 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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C.S. Aravinda, F.T. Farrell, Exotic negatively curved structures on Cayley hyperbolic manifolds, Jour. Differential Geom. 63 (2003), 41-62.

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C.S. Aravinda, F.T. Farrell, Exotic structures and quaternionic hyperbolic manifolds, to appear in Proc. of the Internat. Conf. on Algebraic groups and Arithmetic, December 17-22, 2001, TIFR, Mumbai.

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P. Petersen, Riemannian Geometry, Graduate Texts in Math., 171, Springer-Verlag, NY, 1998. MR 98m:53001

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K. Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. Math. 135 (1992), 165-182. MR 92m:57048

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J. Jost, S.-T. Yau, Harmonic maps and superrigidity, Proc. Sympos. Pure Math., 54, Part 1, 245-280, Amer. Math. Soc., Providence, RI, 1993. MR 94m:58060

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N. Mok, Y.-T. Siu, S.-K. Yeung, Geometric superrigidity, Invent. Math. 113 (1993), 57-83. MR 94h:53079

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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: 10.1090/S0002-9939-04-07531-8
PII: S 0002-9939(04)07531-8
Received by editor(s): September 18, 2003
Posted: 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 of article: Copyright 2004, American Mathematical Society

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