p-Metrics on GL(n,C)/Un and their Busemann compactifications

✍ Scribed by Shmuel Friedland; Pedro J. Freitas

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 275 KB
• Volume: 376
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(03)00661-x

✦ Synopsis

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 pnorms 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.