P-Metrics on [formula omitted] and their Busemann compactifications

Abstract

Let GL (n, C)⊃ U n 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 X n= GL (n, C)/ U n for p∈[1,∞], which are induced by Schatten p-norms on the tangent bundle of X n and are invariant under the action of GL (n, C) . 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.