Model-surface method: an infinite-dimensional version
type: Item
instance of: scholarly article
title: Model-surface method: an infinite-dimensional version
zbMATH Open document ID: 1302.32039
DOI: 10.1134/S0081543812080032
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2014-10-09T00:00:00Z
review text: A `model surface' is a homogeneous real-algebraic submanifold of the complex space \(\mathbb C^N\) that strongly osculates a real submanifold of \(\mathbb C^N\). The most common case is a hermitian quadric modelled on the Levi form of a real submanifold in complex space. The geometry of model surfaces is rather transparent and it governs the geometry of more general submanifolds. In particular, the (infinitesimal) automorphisms of a germ of a manifold can be represented as a sub-Lie algebra of the automorphisms of the corresponding model surface. In the paper under review the author generalizes some notions and results on model surfaces to the infinite dimensional case. Most of the facts transfer literally. However non-degenerate Levi-Tanaka algebras now may be of infinite depth.
reviewed by: Gerd Schmalz
Mathematics Subject Classification ID: 32V99
zbMATH DE Number: 6353214
zbMATH Keywords: CR-manifolds
zbMATH Keywords: Levi-Tanaka algebra
zbMATH Keywords: Hilbert space
author: Valeriĭ K. Beloshapka
MaRDI profile type: Publication
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full work available at URL: s0081543812080032
OpenAlex ID: W2068119564
description: scientific article; zbMATH DE number 6353214