A new look at adapted complex structures
type: Item
instance of: scholarly article
title: A new look at adapted complex structures
zbMATH Open document ID: 1252.32029
author: Róbert Szőke
author: László Lempert
published in: Bulletin of the London Mathematical Society
publication date: 2012-04-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1004.4069
Mathematics Subject Classification ID: 32Q15
Mathematics Subject Classification ID: 32G05
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 6023881
zbMATH Keywords: Grauert tube
zbMATH Keywords: Kähler structure
zbMATH Keywords: polarization
zbMATH Keywords: geometric quantization
MaRDI profile type: Publication
OpenAlex ID: W1974387921
arXiv ID: 1004.4069
DOI: 10.1112/BLMS/BDR097
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review text: 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.
reviewed by: Boris Kruglikov
description: scientific article; zbMATH DE number 6023881