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

   

 

Rigidity of some Weyl manifolds with nonpositive sectional curvature


Author: Maciej P. Wojtkowski
Journal: Proc. Amer. Math. Soc. 133 (2005), 3395-3402
MSC (2000): Primary 53C99, 37Dxx
Published electronically: June 20, 2005
MathSciNet review: 2161165
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Abstract: We provide a list of all locally metric Weyl connections with nonpositive sectional curvatures on two types of manifolds, $n$-dimensional tori $\mathbb{T}^{n}$and $\mathbb{M}^{n} =\mathbb{S}^{1}\times \mathbb{S}^{n-1}$ with the standard conformal structures. For $\mathbb{M}^{n}$ we prove that it carries no other Weyl connections with nonpositive sectional curvatures, locally metric or not. In the case of $\mathbb{T}^{n}$ we prove the same in the more narrow class of integrable connections.


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Additional Information

Maciej P. Wojtkowski
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Email: maciejw@math.arizona.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07809-3
PII: S 0002-9939(05)07809-3
Keywords: Weyl connection, nonpositive sectional curvature
Received by editor(s): April 11, 2003
Received by editor(s) in revised form: April 12, 2004
Published electronically: June 20, 2005
Additional Notes: The author is grateful to Leonid Friedlander, Feliks Przytycki, Don Wang and the referee for their comments.
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2005 by the author