Equidistant Hypersurfaces Of The Complex Bidisk ℍ²_ℂ× ℍ²_ℂ

2025/05/28 by Gongopadhyay, Krishnendu, Kundu, Lokenath, Tiwari, Aditya
#51M10 #53A35 #57M50 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2505.22562

Abstract

We consider the isometries of the complex hyperbolic bidisk, that is, the product space ℍ²_ℂ × ℍ²_ℂ , where each factor ℍ²_ℂ denotes the complex hyperbolic plane. We investigate the Dirichlet domain formed by the action of a cyclic subgroup (g₁, g₂), where each g_i is loxodromic. We prove that such a Dirichlet domain has two sides.

Citations

• Equidistant hypersurfaces of the bidisk

Related

• Hyperkaehler Marriage of the two sphere with the hyperbolic space
• Dirichlet-Ford domains and Double Dirichlet domains
• Complex hyperbolic equidistant loci
• Complex hyperbolic 2-orbifolds with isolated singularities
• Conjugation Orbits of Loxodromic Pairs in SU(n,1)