LeBrun's nonrealizability theory in higher dimensions
type: Item
instance of: scholarly article
title: LeBrun's nonrealizability theory in higher dimensions
zbMATH Open document ID: 0573.32018
DOI: 10.1215/S0012-7094-85-05222-6
author: Hugo Rossi
published in: Duke Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: In this article, the assertions made by \textit{C. R. LeBrun} in the last paragraph of his paper in Trans. Am. Math. Soc. 278, 209-231 (1983; Zbl 0562.53018) are verified. Associated to every Riemannian manifold (M,g) is a CR manifold N, where N is the space of g-isotropic lines in the complexified cotangent bundle \(T^*M\) and the distribution defining the CR structure is given by the vanishing of the canonical symplectic form on \(T^*M\). It is shown that N is determined only by the conformal structure underlying (M,g), and N can be locally embedded in a complex manifold if and only if (M,g) is conformally equivalent to a real- analytic Riemannian manifold.
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32G07
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 32C05
Mathematics Subject Classification ID: 32Q99
zbMATH DE Number: 3914707
zbMATH Keywords: nonrealizability theorem of LeBrun
zbMATH Keywords: Cauchy-Riemann embedding
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: CR manifold
zbMATH Keywords: conformal structure
MaRDI profile type: Publication
cites work: Holomorphic extension of CR functions
cites work: Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné
cites work: Non-realizable CR structures
cites work: A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds
cites work: On maximal families of compact complex submanifolds of complex manifolds
cites work: Vector bundles on complex projective spaces
full work available at URL: s0012-7094-85-05222-6
OpenAlex ID: W2058643184
description: scientific article; zbMATH DE number 3914707