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- W2540410285 abstract "We study general properties of images of holomorphic isometric embeddings of complex unit balls ({mathbb {B}}^m) into irreducible bounded symmetric domains ({varOmega }) of rank at least 2. In particular, we show that such holomorphic isometries with the minimal normalizing constant arise from linear sections ({varLambda }) of the compact dual (X_c) of ({varOmega }). The question naturally arises as to which linear sections (Z = {varLambda }cap {varOmega }) are actually images of holomorphic isometries of complex unit balls. We study the latter question in the case of bounded symmetric domains ({varOmega }) of type IV, alias Lie balls, i.e., bounded symmetric domains dual to hyperquadrics. We completely classify images of all holomorphic isometric embeddings of complex unit balls into such bounded symmetric domains ({varOmega }). Especially we show that there exist holomorphic isometric embeddings of complex unit balls of codimension 1 incongruent to the examples constructed by Mok (Proc Am Math Soc 144:4515–4525, 2016) from varieties of minimal rational tangents, and that moreover any holomorphic isometric embedding (f: {mathbb {B}}^m rightarrow {varOmega }) extends to a holomorphic isometric embedding (f: mathbb B^{n-1} rightarrow {varOmega }), (dim {varOmega }= n). The case of Lie balls is particularly relevant because holomorphic isometric embeddings of complex unit balls of sufficiently large dimensions into an irreducible bounded symmetric domain other than a type-IV domain are expected to be more rigid." @default.
- W2540410285 created "2016-11-04" @default.
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- W2540410285 date "2016-10-31" @default.
- W2540410285 modified "2023-10-01" @default.
- W2540410285 title "Holomorphic isometries of $${mathbb {B}}^m$$ B m into bounded symmetric domains arising from linear sections of minimal embeddings of their compact duals" @default.
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- W2540410285 doi "https://doi.org/10.1007/s00209-016-1778-7" @default.
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