Monotonicity for the Chern-Moser-Weyl curvature tensor and CR embeddings
type: Item
instance of: scholarly article
title: Monotonicity for the Chern-Moser-Weyl curvature tensor and CR embeddings
zbMATH Open document ID: 1202.32016
author: Yuan Zhang
author: Xiaojun Huang
published in: Science in China. Series A
publication date: 2010-07-24T00:00:00Z
review text: \textit{S. M. Webster} [Duke Math. J. 45, No. 1, 39--46 (1978; Zbl 0373.32012)] showed that any nondegenerate hypersurface in \(\mathbb{C}^{n+1}\), having signature \(\ell\), can be embedded into the hyperquadric \(\mathbf{H}^{n+2}_{\ell+1}\subset\mathbb{C}^{n+2}\), of signature \(\ell+1\). Here the authors prove that, in general, there is no embedding in a quadric \(\mathbf{H}^{N+1}_{\ell}\subset\mathbb{C}^{N+1}\) of the same signature \(\ell\), even taking very large \(N\). This result, that does not apply to the pseucoconvex case (\(\ell=0\)) is obtained by proving a monotonicity result for the Chern-Moser-Weyl curvature tensor, under \(CR\) embeddings, along the complex directions that are isotropic for the Levi form.
reviewed by: Mauro Nacinovich
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 32V05
Mathematics Subject Classification ID: 32V30
zbMATH DE Number: 5760408
zbMATH Keywords: Chern-Moser-Weyl curvature tensor
zbMATH Keywords: \(CR\) embedding
zbMATH Keywords: curvature decreasing property
MaRDI profile type: Publication
full work available at URL: s11425-009-0204-6
OpenAlex ID: W2268053127
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DOI: 10.1007/S11425-009-0204-6
description: scientific article; zbMATH DE number 5760408