On structures of normal forms of complex points of small C$^2$-perturbations of real 4-manifolds embedded in a complex 3-manifold

Starčič, Tadej (author)

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.

• Language: English
• Keywords: CR manifolds, closure graphs, complex points, normal forms, perturbations
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 43 str.
• Numbering: Vol. 118, iss. 2, art. 48
• PID: 20.500.12556/RUL-156092
• UDC: 517.5
• ISSN on article: 1578-7303
• DOI: 10.1007/s13398-023-01545-0
• COBISS.SI-ID: 194449155
• Publication date in RUL: 10.05.2024

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: Springer Nature, Real Academia de Ciencias Exactas, Físicas y Naturales
• ISSN: 1578-7303
• COBISS.SI-ID: 17645351

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
• Keywords: CR mnogoterosti, grafi zaprtja, kompleksne točke, normalne forme, perturbacije

Projects

• 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