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Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 1, Pages 56–64
DOI: https://doi.org/10.4213/faa96 (Mi faa96) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Circles and Clifford Algebras

V. A. Timorinab

a University of Toronto
b Independent University of Moscow
Full-text PDF (178 kB) Citations (4)
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DOI: https://doi.org/10.4213/faa96
Abstract: Consider a smooth map of a neighborhood of the origin in a real vector space into a neighborhood of the origin in a Euclidean space. Suppose that this map takes all germs of lines passing through the origin to germs of Euclidean circles, or lines, or a point. We prove that under some simple additional assumptions this map takes all lines passing though the origin to the same circles as a Hopf map coming from a representation of a Clifford algebra. We also describe a connection between our result and the Hurwitz–Radon theorem about sums of squares.
Keywords: line, circle, Clifford algebra, Hopf map.
Received: 31.10.2002
English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 1, Pages 45–51
DOI: https://doi.org/10.1023/B:FAIA.0000024867.02438.e3
Bibliographic databases:
Document Type: Article
UDC: 514.752.24+514.744.2
Language: Russian
Citation: V. A. Timorin, “Circles and Clifford Algebras”, Funktsional. Anal. i Prilozhen., 38:1 (2004), 56–64; Funct. Anal. Appl., 38:1 (2004), 45–51
Citation in format AMSBIB
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  • https://doi.org/10.4213/faa96
  • https://www.mathnet.ru/eng/faa/v38/i1/p56
    • This publication is cited in the following 4 articles:
    1. Vsevolod Petrushchenko, Vladlen Timorin, “On Maps Taking Lines to Plane Curves”, Arnold Math J., 2:1 (2016), 1  crossref
    2. Timorin V., “Planarizations and Maps Taking Lines to Linear Webs of Conics”, Math. Res. Lett., 19:4 (2012), 899–907  crossref  mathscinet  zmath  isi  elib  scopus
    3. Izadi F., “Rectification of spheres of co-dimension 1 and 2 in Rn”, Differential Geom. Appl., 27:1 (2009), 15  crossref  mathscinet  zmath  isi  elib  scopus
    4. Timorin V., “Circles and quadratic maps between spheres”, Geom. Dedicata, 115:1 (2005), 19–32  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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