Hypersurfaces through higher-codimensional submanifolds of \(\mathbb{C}^n\) with preserved Levi-kernel
type: Item
instance of: scholarly article
title: Hypersurfaces through higher-codimensional submanifolds of \(\mathbb{C}^n\) with preserved Levi-kernel
zbMATH Open document ID: 0899.32005
DOI: 10.1007/BF02760928
author: Giuseppe Zampieri
published in: Israel Journal of Mathematics
publication date: 1998-11-09T00:00:00Z
review text: Let \(S\) be a submanifold of a complex manifold \(X,\) and assume that \(S\) is generic, i.e. \(TS+\sqrt{-1}TS=TX\). The author shows that one may construct a hypersurface \(M\supset S\) with Levi-form \(L_M\) with as many negative (or positive) eigenvalues as \(L_S\), the Levi-form of \(S\), at a prescribed conormal. When \(\text{rank }L_S\) is constant, he shows that \(M\) can be found such that \(L_M\) and \(L_S\) have the same number of negative eigenvalues at any common conormal, and in this last case, he discusses the relation between complex submanifolds of \(S\) whose tangent plane belongs to the null-space of \(L_S\) and complex submanifolds of \(\dot T_S^*X\). He finally applies this construction to propagation of micro-analyticity of CR-hyperfunctions along complex, \(L_S\)-null, curves.
Mathematics Subject Classification ID: 32V05
zbMATH DE Number: 1123742
zbMATH Keywords: Levi-form
zbMATH Keywords: CR-hyperfunctions
reviewed by: Alberto Parmeggiani
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02760928
OpenAlex ID: W2321856550
description: scientific article; zbMATH DE number 1123742