Pré-Publication, Document De Travail Année : 2024

Distance-preserving maps between bounded symmetric domains

Résumé

We study the rigidity of maps between bounded symmetric domains that preserve the Carathéodory/Kobayashi metric. We show that such maps are only possible when the rank of the codomain is at least as great as that of the domain. When the ranks are equal, and the domain is irreducible, we show that the map is either holomorphic or antiholomorphic. In the holomorphic case, we show that the map is in fact a triple homomorphism, under the additional assumption that the origin is mapped to the origin.
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Dates et versions

hal-04911597 , version 1 (24-01-2025)

Identifiants

  • HAL Id : hal-04911597 , version 1

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Bas Lemmens, Cormac Walsh. Distance-preserving maps between bounded symmetric domains. 2024. ⟨hal-04911597⟩
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