On isometries of the Carathéodory and Kobayashi metrics on strongly pseudoconvex domains
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چکیده
Let 1 and 2 be strongly pseudoconvex domains in Cn and f : 1 → 2 an isometry for the Kobayashi or Carathéodory metrics. Suppose that f extends as a C1 map to ̄1. We then prove that f |∂ 1 : ∂ 1 → ∂ 2 is a CR or anti-CR diffeomorphism. It follows that 1 and 2 must be biholomorphic or anti-biholomorphic. Mathematics Subject Classification (2000): 32F45 (primary); 32Q45 (secondary).
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