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

Seshadri, Harish and Verma, Kaushal (2006) On isometries of the Caratheodory and Kobayashi metrics on strongly pseudoconvex domains. In: Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, 5 (3). pp. 393-417.

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Abstract

Let \Omega(1) and \Omega(2) be strongly pseudoconvex domains in C-n and f : \Omega(1) --> \Omega(2) an isometry for the Kobayashi or Caratheodory metrics. Suppose that f extends as a C-1 map to (\Omega) over bar (1). We then prove that f\textbackslash{}partial derivative \Omega(1) : partial derivative \Omega(1) --> partial derivative \Omega(2) is a CR or anti-CR diffeomorphism. It follows that \Omega(1) and \Omega(2) must be biholomorphic or anti-biholomorphic.

Item Type: Journal Article http://www.numdam.org/numdam-bin/feuille... Division of Physical & Mathematical Sciences > Mathematics 22 Jul 2008 30 Jun 2012 08:03 http://eprints.iisc.ernet.in/id/eprint/15198