A new look at adapted complex structures (Q2880386)
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scientific article; zbMATH DE number 6023881
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new look at adapted complex structures |
scientific article; zbMATH DE number 6023881 |
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A new look at adapted complex structures (English)
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13 April 2012
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Grauert tube
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Kähler structure
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polarization
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geometric quantization
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0.81805384
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0.79460573
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0.79334897
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0.7926225
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0.7883887
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On a closed real analytic Riemannian manifold a one-parameter family of adapted complex structures on the total space of the tangent bundle is constructed. For parameters \(s\in \mathbb C\setminus\mathbb R\), this is a Kähler structure, which for the particular value \(s=i\) was investigated before by \textit{V. Guillemin} and \textit{M. Stenzel} [J. Differ. Geom. 34, No. 2, 561--570 (1991; Zbl 0746.32005)] and \textit{L. Lempert} and \textit{R. Szőke} [Math. Ann. 290, No. 4, 689--712 (1991; Zbl 0752.32008)]. For real parameters \(s\), the structure is real polarized. The results are announced to be applicable to geometric quantization.
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