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}, zbl = {1170.32309}, mrnumber = {2274785}, language = {en}, url = {http://archive.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 DA - 2006/// SP - 393 EP - 417 VL - Ser. 5, 5 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2006_5_5_3_393_0/ UR - https://zbmath.org/?q=an%3A1170.32309 UR - https://www.ams.org/mathscinet-getitem?mr=2274785 LA - en ID - ASNSP_2006_5_5_3_393_0 ER -
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://archive.numdam.org/item/ASNSP_2006_5_5_3_393_0/
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