Please use this identifier to cite or link to this item:
Title: Normal Forms and Symmetries of Real Hypersurfaces of Finite Type in C²
Contributor(s): Ezhov, Vladimir (author); Kolar, Martin (author); Schmalz, Gerd  (author)orcid 
Publication Date: 2013
DOI: 10.1512/iumj.2013.62.4833
Handle Link:
Abstract: We give a complete description of normal forms for real hypersurfaces of finite type in C² with respect to their holomorphic symmetry algebras. The normal forms include refined versions of the constructions by Chern-Moser [6], Stanton [20], Kolář [14]. We use the method of simultaneous normalisation of the equations and symmetries that goes back to Lie and Cartan. Our approach leads to a unique canonical equation of the hypersurface for every type of its symmetry algebra. Moreover, even in the Levi-degenerate case, our construction implies convergence of the transformation to the normal form if the dimension of the symmetry algebra is at least two. We illustrate our results by explicitly normalising Cartan's homogeneous hypersurfaces and their automorphisms.
Publication Type: Journal Article
Grant Details: ARC/DP130103485
Source of Publication: Indiana University Mathematics Journal, 62(1), p. 1-32
Publisher: Indiana University
Place of Publication: United States of America
ISSN: 0022-2518
Field of Research (FOR): 010111 Real and Complex Functions (incl Several Variables)
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
Statistics to Oct 2018: Visitors: 135
Views: 141
Downloads: 1
Appears in Collections:Journal Article

Files in This Item:
2 files
File Description SizeFormat 
Show full item record


checked on Nov 30, 2018

Page view(s)

checked on Mar 4, 2019
Google Media

Google ScholarTM



Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.