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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Hyperbolic rank of products


Authors: Thomas Foertsch and Viktor Schroeder
Journal: Proc. Amer. Math. Soc. 133 (2005), 557-563
MSC (2000): Primary 53C20
Published electronically: August 25, 2004
MathSciNet review: 2093080
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Abstract | References | Similar Articles | Additional Information

Abstract: Generalizing a result of Brady and Farb (1998), we prove the existence of a bilipschitz embedded manifold of negative curvature bounded away from zero and dimension $m_1+m_2-1$ in the product $X:=X_1^{m_1}\times X_2^{m_2}$ of two Hadamard manifolds $X_i^{m_i}$ of dimension $m_i$ with negative curvature bounded away from zero.

Combining this result with a result of Buyalo and Schroeder (2002), we prove the additivity of the hyperbolic rank for products of manifolds with negative curvature bounded away from zero.


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Additional Information

Thomas Foertsch
Affiliation: Universität Zürich, Mathematisches Institut, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
Address at time of publication: Department of Mathematics, University of Michigan, 525 E University Avenue, East Hall, Ann Arbor, Michigan 48109-1109
Email: foertsch@math.unizh.ch

Viktor Schroeder
Affiliation: Universität Zürich, Mathematisches Institut, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
Email: vschroed@math.unizh.ch

DOI: https://doi.org/10.1090/S0002-9939-04-07598-7
Keywords: Hadamard manifolds, hyperbolic rank
Received by editor(s): December 19, 2001
Received by editor(s) in revised form: April 29, 2003
Published electronically: August 25, 2004
Additional Notes: The first author was supported by the SNF Grant 21 - 589 38.99
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2004 American Mathematical Society