Compact Heisenberg manifolds as CR manifolds
type: Item
instance of: scholarly article
title: Compact Heisenberg manifolds as CR manifolds
zbMATH Open document ID: 1067.32025
DOI: 10.1007/BF02922102
published in: The Journal of Geometric Analysis
publication date: 2004-11-23T00:00:00Z
review text: Let \(H_d\) be the (2d+1)-dimensional Heisenberg group, and \(\Gamma\) be a lattice subgroup of it such that the quotient space \(M=\Gamma \setminus H_d\) is compact. Then there is a natural strongly pseudoconvex CR structure on M. Firstly, studying the Fourier analysis on this strongly pseudoconvex CR manifold M, the eigenvalues and eigenforms of the Kohn Laplacian are calculated completely. Secondly, a realization of M as the boundary of a bounded domain in a line bundle over an Abelian variety is obtained, that is: M is in one-to-one correspondence, up to holomorphic/CR equivalence, with the Abelian variety \(C^d / \Lambda\) equipped with a positive line bundle, where \(\Lambda=\pi(\Gamma)\), \(\pi\) is the quotient mapping.
reviewed by: Na Jisheng
Mathematics Subject Classification ID: 32V15
Mathematics Subject Classification ID: 32V20
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 2118174
zbMATH Keywords: CR manifold
zbMATH Keywords: Heisenberg group
zbMATH Keywords: Kohn Laplacian
zbMATH Keywords: Abelian variety
author: Gerald B. Folland
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02922102
OpenAlex ID: W2058490796
description: scientific article; zbMATH DE number 2118174