Explicit expression of Cartan's connection for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere
type: Item
instance of: scholarly article
title: Explicit expression of Cartan's connection for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere
zbMATH Open document ID: 1262.32040
author: Joël Merker
author: Masoud Sabzevari
published in: Central European Journal of Mathematics
publication date: 2013-02-18T00:00:00Z
review text: Let \(M^3 \subset {\mathbb{C}}^2\) be a \(C^6\)-smooth Levi-nondegenerate hypersurface defined as the graph of a function \(v = \varphi(x,y,u)\). The authors study the Cartan geometry of such manifolds, and present a so-called curvature function of a related Tanaka-type normal connection. All elements of the connection are completely effective in terms of the graphing function \(\varphi\). The authors prove that the vanishing of this curvature function explicitly characterizes the local biholomorphic equivalence of such \(M\) and the Heisenberg sphere. These \(M\) are then necessarily real-analytic.
Mathematics Subject Classification ID: 32V25
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 58A15
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 16W25
zbMATH DE Number: 6137088
zbMATH Keywords: Cartan connection
zbMATH Keywords: Heisenberg sphere
zbMATH Keywords: cohomology of Lie algebras
zbMATH Keywords: infinitesimal CR automorphisms
zbMATH Keywords: differential algebra
zbMATH Keywords: curvature function
zbMATH Keywords: Bianchi identities
reviewed by: Jiri Lebl
MaRDI profile type: Publication
full work available at URL: s11533-012-0052-4
OpenAlex ID: W2038383047
Wikidata QID: Q126138757
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DOI: 10.2478/S11533-012-0052-4
description: scientific article; zbMATH DE number 6137088