Conjugation Orbits of Loxodromic Pairs in SU(n,1)

2017/05/30 by Krishnendu Gongopadhyay, Gongopadhyay, Krishnendu, Shiv Parsad +1
Mathematics · #15B57 #51M10 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Primary 20H10 #Secondary 30F40

paper · pdf · doi:10.48550/arxiv.1705.10469

openalex publication_date 2017/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \bf H_{\mathbb C}ⁿ be the n-dimensional complex hyperbolic space and \rm SU(n,1) be the (holomorphic) isometry group. An element g in \rm SU(n,1) is called loxodromic or hyperbolic if it has exactly two fixed points on the boundary ∂ \bf H_{\mathbb C}ⁿ. We classify \rm SU(n,1) conjugation orbits of pairs of loxodromic elements in \rm SU(n,1).

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