Poincaré automorphisms for nondegenerate CR quadrics
type: Item
instance of: scholarly article
title: Poincaré automorphisms for nondegenerate CR quadrics
zbMATH Open document ID: 0847.32015
DOI: 10.1007/BF01459726
author: Vladimir Ejov
author: Gerd Schmalz
published in: Mathematische Annalen
publication date: 1996-10-15T00:00:00Z
full work available at URL: https://eudml.org/doc/165162
review text: Let \(\langle , \rangle\) be (a nondegenerate vector valued Levi form, i.e.) an \(\mathbb{R}^k\) valued Hermitian form in \(\mathbb{C}^n\) satisfying (i) if \(\langle z, b \rangle = 0\) for all \(z\) in \(\mathbb{C}^n\), then \(b = 0\); (ii) if \(f (\langle z,z \rangle) \equiv 0\) for some linear functional \(f\) in \((\mathbb{R}^k)'\), then \(f = 0\). The set \(Q = \{(z,w)\) in \(\mathbb{C}^n \times \mathbb{C}^k \mid \text{Im} (w) = \langle z,z \rangle\}\) is said to be a nondegenerate quadric in \(\mathbb{C}^{n + k}\). The authors study some automorphisms of \(Q\) which are called Poincaré automorphisms, and furnish some explicit formulas for them. Moreover they show that such automorphisms generalize linear fractional transformations. The last part of the paper is devoted to the discussion of some questions concerning automorphisms of quadrics.
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 14J50
Mathematics Subject Classification ID: 11E12
zbMATH DE Number: 537308
zbMATH Keywords: nondegenerate CR quadrics
zbMATH Keywords: Poincaré automorphisms
reviewed by: Cristina Turrini
MaRDI profile type: Publication
cites work: On the analyticity of CR mappings
cites work: Q4200895
cites work: A uniqueness theorem for automorphisms of a nondegenerate surface in a complex space
cites work: Real hypersurfaces in complex manifolds
cites work: Mappings of quadric Cauchy-Riemann manifolds
cites work: On the pseudo-conformal geometry of hypersurface of the space of \(n\) complex variables
OpenAlex ID: W1988583760
description: scientific article; zbMATH DE number 537308