Let and be domains in and an isometry for the Kobayashi or Carathéodory metrics. Suppose that extends as a map to . We then prove that is a CR or anti-CR diffeomorphism. It follows that and must be biholomorphic or anti-biholomorphic.
@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}, pages = {393--417}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 5}, number = {3}, year = {2006}, mrnumber = {2274785}, zbl = {1170.32309}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2006_5_5_3_393_0/} }
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 SP - 393 EP - 417 VL - 5 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2006_5_5_3_393_0/ LA - en ID - ASNSP_2006_5_5_3_393_0 ER -
%0 Journal Article %A Seshadri, Harish %T On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2006 %P 393-417 %V 5 %N 3 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2006_5_5_3_393_0/ %G en %F 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, Série 5, Tome 5 (2006) no. 3, pp. 393-417. http://www.numdam.org/item/ASNSP_2006_5_5_3_393_0/
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