On the holomorphicity of isometries of intrinsic metrics in complex analysis

2005/05/13 by Seshadri, Harish, Kaushal Verma, Verma, Kaushal · 1 citation
Mathematics · #32T15 #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/0505284

openalex publication_date 2005/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let \1 and \2 be \s domains in \Cn and f: \1 \rt \2 an isometry for the Kobayashi or Carathéodory metrics. Suppose that f extends as a C¹ map to \om₁. We then prove that f|_{∂ \1}: ∂ \1 \rt ∂ \2 is a CR or anti-CR diffeomorphism. It follows that \1 and \2 must be biholomorphic or anti-biholomorphic. The main tool is a metric version of the Pinchuk rescaling technique.

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• A Kobayashi metric version of Bun Wong's theorem

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