# The hyperbolic rank of homogeneous Hadamard manifolds

Foertsch, T (2002). The hyperbolic rank of homogeneous Hadamard manifolds. Manuscripta Mathematica, 109(1):109-120.

## Abstract

From results in [BrFa] it follows that for Riemannian products of real hyperbolic spaces the sum of the Euclidean rank and the hyperbolic rank is at least the product's dimension. In [Leu] the author proved that, more generally, the same holds for symmetric spaces of non-compact type. In this paper we prove the analogue statement for arbitrary homogeneous Hadamard manifolds.

## Abstract

From results in [BrFa] it follows that for Riemannian products of real hyperbolic spaces the sum of the Euclidean rank and the hyperbolic rank is at least the product's dimension. In [Leu] the author proved that, more generally, the same holds for symmetric spaces of non-compact type. In this paper we prove the analogue statement for arbitrary homogeneous Hadamard manifolds.

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