p-metrics on GL(n, C)/Un and their Busemann compactifications
نویسندگان
چکیده
Let GL(n, C) ⊃ Un 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 Xn = GL(n, C)/Un for p ∈ [1,∞], which are induced by Schatten p-norms on the tangent bundle of Xn 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. 1
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