On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains

Harish Seshadri

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2006)

  • Volume: 5, Issue: 3, page 393-417
  • ISSN: 0391-173X

Abstract

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Let Ω 1 and Ω 2 be strongly pseudoconvex domains in ℂ n and f : Ω 1 → Ω 2 an isometry for the Kobayashi or Carathéodory metrics. Suppose that f extends as a C 1 map to Ω ¯ 1 . We then prove that f | ∂ Ω 1 : ∂ Ω 1 → ∂ Ω 2 is a CR or anti-CR diffeomorphism. It follows that Ω 1 and Ω 2 must be biholomorphic or anti-biholomorphic.

How to cite

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Seshadri, Harish. "On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 5.3 (2006): 393-417. <http://eudml.org/doc/240414>.

@article{Seshadri2006,
abstract = {Let $\Omega _1$ and $\Omega _2$ be $\rm strongly \ pseudoconvex $ domains in $\mathbb \{C\}^n$ and $f: \Omega _1 \rightarrow \Omega _2$ an isometry for the Kobayashi or Carathéodory metrics. Suppose that $f$ extends as a $C^1$ map to $ \bar\{\Omega \}_1$. We then prove that $f|_\{\partial \Omega _1\}: \partial \Omega _1 \rightarrow \partial \Omega _2$ is a CR or anti-CR diffeomorphism. It follows that $\Omega _1$ and $\Omega _2$ must be biholomorphic or anti-biholomorphic.},
author = {Seshadri, Harish},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {393-417},
publisher = {Scuola Normale Superiore, Pisa},
title = {On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains},
url = {http://eudml.org/doc/240414},
volume = {5},
year = {2006},
}

TY - JOUR
AU - Seshadri, Harish
TI - On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2006
PB - Scuola Normale Superiore, Pisa
VL - 5
IS - 3
SP - 393
EP - 417
AB - Let $\Omega _1$ and $\Omega _2$ be $\rm strongly \ pseudoconvex $ domains in $\mathbb {C}^n$ and $f: \Omega _1 \rightarrow \Omega _2$ an isometry for the Kobayashi or Carathéodory metrics. Suppose that $f$ extends as a $C^1$ map to $ \bar{\Omega }_1$. We then prove that $f|_{\partial \Omega _1}: \partial \Omega _1 \rightarrow \partial \Omega _2$ is a CR or anti-CR diffeomorphism. It follows that $\Omega _1$ and $\Omega _2$ must be biholomorphic or anti-biholomorphic.
LA - eng
UR - http://eudml.org/doc/240414
ER -

References

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