Null-quadrics of codimension 4 in \(\mathbb{C}^7\)
type: Item
instance of: scholarly article
title: Null-quadrics of codimension 4 in \(\mathbb{C}^7\)
zbMATH Open document ID: 0920.32008
DOI: 10.1007/BF02361291
author: E. G. Anisova
published in: Mathematical Notes
publication date: 1999-08-31T00:00:00Z
review text: The author classifies the null-quadrics of type (4,3) and finds their automorphism groups. Any null-quadric of codimension 4 in \(\mathbb C^7\) is equivalent either to the quadric \(Q_1\) or to the quadric \(Q_2,\) where \[ \langle z,z\rangle^1_1=2 \text{Re} z^1z^3, \langle z,z\rangle^2_1=2 \text{Re} z^2z^3, \langle z,z\rangle^3_1=2 \text{Im} z^1z^3, \langle z,z\rangle^4_1=2 \text{Im} z^2z^3, \] \[ \langle z,z\rangle^1_2=2 \text{Re} z^1z^3, \langle z,z\rangle^2_2=2 \text{Re} z^2z^3, \langle z,z\rangle^3_2=| z^3|^2, \langle z,z\rangle^4_2=2 \text{Im} z^2z^3. \] The quadrics \(Q_1\) and \(\mathbb Q_2\) are not equivalent.
Mathematics Subject Classification ID: 32V99
Mathematics Subject Classification ID: 14H37
Mathematics Subject Classification ID: 14J50
Mathematics Subject Classification ID: 14E07
zbMATH DE Number: 1257153
zbMATH Keywords: real analytic CR-manifold
zbMATH Keywords: tangent quadrics
zbMATH Keywords: null-quadrics
zbMATH Keywords: automorphism groups
zbMATH Keywords: holomorphic automorphisms
MaRDI profile type: Publication
cites work: Q3791444
cites work: Description of the algebra of infinitesimal automorphisms of quadrics of codimension two and their classification
cites work: Real quadrics of codimension 3 in $ \mathbb C^6$ and their non-linear automorphisms
cites work: On the Equivalence of Pencils of Hermitian Forms
description: scientific article; zbMATH DE number 1257153