Hyperbolic rank of products

Foertsch, Thomas; Schroeder, Viktor

doi:10.1090/S0002-9939-04-07598-7

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.

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