p-Metrics on and their Busemann compactifications

Let be the group of n×n complex valued invertible matrices and the subgroup of unitary matrices respectively. In this paper we study Finsler p-metrics on the homogeneous space for p [1,∞], which are induced by Schatten p-norms on the tangent bundle of Xn and are invariant under the action of . We show that for p (1,∞) the Busemann p-compactification is the visual compactification. For p=1,∞ the Busemann p-compactification is not the visual compactification. We give a complete description of Busemann 1-compactification.