2025/06/11 by Hiroyasu Satoh, Hemangi Madhusudan Shah, Satoh, Hiroyasu +1
Mathematics · #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2506.09710
We prove that every conformal vector field on the complex hyperbolic space ℂHn is Killing for all n≥ 2. Although this rigidity is classically known, our proof is entirely different in nature: it is local, analytic, and fully constructive. Our approach is local, analytic, and constructive: we view ℂH2 through its solvable Lie group model and express the conformal Killing equation as an explicit system of partial differential equations. By solving this system completely, we show that any conformal vector field must be determined by a Killing field. The analysis in complex dimension 2 naturally extends to arbitrary n, yielding a unified and fully explicit proof of this rigidity phenomenon.