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

Seshadri, Harish

Seshadri, Harish

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 5 (2006) no. 3, p. 393-417

Abstract

Let $Ω_{1}$ and $Ω_{2}$ be $strongly pseudoconvex$ domains in $ℂ^{n}$ and $f : Ω_{1} \to Ω_{2}$ an isometry for the Kobayashi or Carathéodory metrics. Suppose that $f$ extends as a $C^{1}$ map to ${\bar{Ω}}_{1}$ . We then prove that ${f |}_{\partial Ω_{1}} : \partial Ω_{1} \to \partial Ω_{2}$ is a CR or anti-CR diffeomorphism. It follows that $Ω_{1}$ and $Ω_{2}$ must be biholomorphic or anti-biholomorphic.

MR 2274785 | Zbl 1170.32309 | 1 citation in Numdam

Classification: 32F45, 32Q45

@article{ASNSP_2006_5_5_3_393_0,
     author = {Seshadri, Harish},
     title = {On isometries of the carath\'eodory and Kobayashi metrics on strongly pseudoconvex domains},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 5},
     number = {3},
     year = {2006},
     pages = {393-417},
     zbl = {1170.32309},
     mrnumber = {2274785},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2006_5_5_3_393_0}
}

Seshadri, Harish. On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 5 (2006) no. 3, pp. 393-417. http://www.numdam.org/item/ASNSP_2006_5_5_3_393_0/

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