Hyperbolic rank of products
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- by Thomas Foertsch and Viktor Schroeder PDF
- Proc. Amer. Math. Soc. 133 (2005), 557-563 Request permission
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.References
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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
- MR Author ID: 157030
- Email: vschroed@math.unizh.ch
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 557-563
- MSC (2000): Primary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-04-07598-7
- MathSciNet review: 2093080