Differential geometry of Cartan domains of type four (Q920418)
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scientific article; zbMATH DE number 4163672
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Differential geometry of Cartan domains of type four |
scientific article; zbMATH DE number 4163672 |
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Differential geometry of Cartan domains of type four (English)
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1990
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A Cartan domain of type IV is a bounded symmetric domain \(D_ n=\{z\in {\mathbb{C}}^ n:\;| z| <1,\quad 1-2| z|^ 2+|^ tzz|^ 2>0\}\) whose Bergman kernel function is \((1-2| z|^ 2+|^ tzz|^ 2)^{-n}.\) The author proves that -2\(\leq (holomorphic\) sectional curvature of \(D_ n)\leq -1\) and -2\(\leq (holomorphic\) bisectional curvature of \(D_ n)\leq 0\). A complete classification for totally geodesic complex submanifolds of \(D_ n\) is also given.
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Cartan domain
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bounded symmetric domain
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Bergman kernel function
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totally geodesic complex submanifolds
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0.7785665392875671
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0.7730081677436829
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