Hyperbolic Rank of Products
Differential Geometry
2007-05-23 v1
Abstract
Generalizing results due to Brady and Farb we prove the existence of a bilipschitz embedded manifold of pinched negative curvature 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 pinched negative curvature. Combining this result with a Theorem by Buyalo and Schroeder we prove the additivity of the hyperbolic rank for products of manifolds with pinched negative curvature.
Keywords
Cite
@article{arxiv.math/0208197,
title = {Hyperbolic Rank of Products},
author = {Thomas Foertsch and Viktor Schroeder},
journal= {arXiv preprint arXiv:math/0208197},
year = {2007}
}
Comments
11 pages