The hyperbolic rank of homogeneous Hadamard manifolds

 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.