Nearly Kählerian embeddings of symplectic manifolds
type: Item
instance of: scholarly article
title: Nearly Kählerian embeddings of symplectic manifolds
zbMATH Open document ID: 0990.53086
author: David Borthwick
author: A. Uribe
published in: The Asian Journal of Mathematics
publication date: 2001-04-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/9812041
review text: Let \(X,\omega\) be a \(2n\)-dimensional compact symplectic manifold without boundary, \(H_k \subset C^\infty (X,L^{\otimes k})\) a suitable sequence of finite dimensional Hilbert spaces defined for all sufficiently large \(k\). This paper studies the asymptotic geometry of the maps \(F_k:X \to\mathbb{P} H_k^*\) obtained by the usual procedure of algebraic geometry. It is shown that the \(F_k\) are projective embeddings which for large \(k\) are `nearly' symplectic as well as `nearly' isometric. The proof parallels that of \textit{S. Zelditch} [Int. Math. Res. Not. 1998, No. 6, 317-331 (1998; Zbl 0922.58082)] to some extent.
reviewed by: Erwin O. Kreyszig
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 32Q60
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 58J40
Mathematics Subject Classification ID: 53D05
zbMATH DE Number: 1585248
zbMATH Keywords: compact symplectic manifold
zbMATH Keywords: asymptotic geometry
zbMATH Keywords: projective embeddings
MaRDI profile type: Publication
arXiv ID: math/9812041
OpenAlex ID: W1653920623
DOI: 10.4310/AJM.2000.V4.N3.A6
description: scientific article; zbMATH DE number 1585248