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Title:On structures of normal forms of complex points of small ${\mathcal C}^2$-perturbations of real $4$-manifolds embedded in a complex $3$-manifold
Authors:ID Starčič, Tadej (Author)
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MD5: 9C59C6A8DB83987EB72B186896A6324E
 
URL URL - Source URL, visit https://link.springer.com/article/10.1007/s13398-023-01545-0
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:We extend our previous result on the behaviour of the quadratic part of a complex points of a small ${\mathcal C}^2$-perturbation of a real $4$-manifold embedded in a complex $3$-manifold. We describe the change of the structure of the quadratic normal form of a complex point. It is an immediate consequence of a theorem clarifying how small perturbations can change the bundle of a pair of one arbitrary and one symmetric $2 \times 2$ matrix with respect to an action of a certain linear group.
Keywords:CR manifolds, closure graphs, complex points, normal forms, perturbations
Publication status:Published
Publication version:Version of Record
Publication date:01.04.2024
Year of publishing:2024
Number of pages:43 str.
Numbering:Vol. 118, iss. 2, [article no.] 48
PID:20.500.12556/DiRROS-18874 New window
UDC:517.5
ISSN on article:1578-7303
DOI:10.1007/s13398-023-01545-0 New window
COBISS.SI-ID:194449155 New window
Note:
Publication date in DiRROS:06.05.2024
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Downloads:282
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Record is a part of a journal

Title:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas
Shortened title:Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat.
Publisher:Real Academia de Ciencias Exactas, Físicas y Naturales
ISSN:1578-7303
COBISS.SI-ID:17645351 New window

Document is financed by a project

Funder:ARRS - Slovenian Research Agency
Project number:P1-0291
Name:Analiza in geometrija

Funder:ARRS - Slovenian Research Agency
Project number:J1-3005
Name:Kompleksna in geometrijska analiza

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

Language:Slovenian
Abstract:V članku razširimo naš prejšnji rezultat, ki opisuje obnašanje kvadratičnega dela kompleksnih točk majhnih ${\mathcal C}^2$-perturbacij realnih $4$-mnogoterosti vloženih v kompleksno $3$-mnogoterost. Opišemo spremembo strukture kvadratične normalne forme kompleksne točke. To je neposredna posledica izreka, ki pojasnjuje, kako lahko majhne perturbacije spremenijo strukturo para ene poljubne in ene simetrične $2 \times 2$ matrike glede na delovanje neke določene linearne grupe.
Keywords:CR mnogoterosti, grafi zaprtja, kompleksne točke, normalne forme, perturbacije


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