Infinitesimal Conformal Rigidity on Damek-Ricci Spaces

2025/07/24 by Hiroyasu Satoh, Hemangi Madhusudan Shah, Satoh, Hiroyasu +1
Computer Science · Mathematics · Physics and Astronomy · #53C24 #53C25 #53C35 #Advanced Differential Geometry Research #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2507.18137

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/31

Abstract

We show that every conformal vector field on a Damek-Ricci space is necessarily Killing, establishing a strong form of infinitesimal conformal rigidity. Although this rigidity phenomenon is classically known in the Einstein setting, our proof follows a completely different approach. We formulate the conformal Killing condition as an explicit system of partial differential equations on the solvable Lie group model and analyze it directly. This local and analytic method yields a constructive proof of rigidity without relying on global arguments or transformation groups.

Citations

• A remark about the Lie algebra of infinitesimal conformal transformations of the Euclidian space

Cited by

• A Constructive Approach to Infinitesimal Conformal Rigidity on Complex Hyperbolic Space

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