Skip to Main Content

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

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Nonpositivity: Curvature vs. curvature operator
HTML articles powered by AMS MathViewer

by C. S. Aravinda and F. T. Farrell PDF
Proc. Amer. Math. Soc. 133 (2005), 191-192 Request permission

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
  • C.S. Aravinda, F.T. Farrell, Exotic negatively curved structures on Cayley hyperbolic manifolds, Jour. Differential Geom. 63 (2003), 41–62.
  • 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.
  • Peter Petersen, Riemannian geometry, Graduate Texts in Mathematics, vol. 171, Springer-Verlag, New York, 1998. MR 1480173, DOI 10.1007/978-1-4757-6434-5
  • Kevin Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. of Math. (2) 135 (1992), no. 1, 165–182. MR 1147961, DOI 10.2307/2946567
  • Jürgen Jost and Shing-Tung Yau, Harmonic maps and superrigidity, Differential geometry: partial differential equations on manifolds (Los Angeles, CA, 1990) Proc. Sympos. Pure Math., vol. 54, Amer. Math. Soc., Providence, RI, 1993, pp. 245–280. MR 1216587
  • Ngaiming Mok, Yum Tong Siu, and Sai-Kee Yeung, Geometric superrigidity, Invent. Math. 113 (1993), no. 1, 57–83. MR 1223224, DOI 10.1007/BF01244302
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32Q05, 53C20
  • Retrieve articles in all journals with MSC (2000): 32Q05, 53C20
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
  • 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