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Matematicheskie Zametki, 2008, Volume 83, Issue 4, Pages 590–605
DOI: https://doi.org/10.4213/mzm4578 (Mi mzm4578) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Combinatorial Construction of Tangent Vector Fields on Spheres

A. A. Ohnikyan

Yerevan State University
Full-text PDF (533 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm4578
Abstract: For every odd n, on the sphere Sn, ρ(n)−1 linear orthonormal tangent vector fields, where ρ(n) is the Hurwitz–Radon number, are explicitly constructed. For each 8×8 sign matrix, compositions for infinite-dimensional positive definite quadratic forms are explicitly constructed. The infinite-dimensional real normed algebras thus arising are proved to have certain properties of associativity and divisibility type.
Keywords: linear orthonormal tangent vector field, odd-dimensional sphere, composition of quadratic forms, Clifford algebra, Hurwitz–Radon theorem, Cayley number.
Received: 28.04.2006
Revised: 22.06.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 4, Pages 539–553
DOI: https://doi.org/10.1134/S0001434608030279
Bibliographic databases:
UDC: 515.164.322
Language: Russian
Citation: A. A. Ohnikyan, “Combinatorial Construction of Tangent Vector Fields on Spheres”, Mat. Zametki, 83:4 (2008), 590–605; Math. Notes, 83:4 (2008), 539–553
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    1. Arizmendi G., Herrera R., “A Binary Encoding of Spinors and Applications”, Complex Manifolds, 7:1 (2020), 162–193  crossref  mathscinet  isi
    2. M. Obiedat, “A Note on the Construction of Complex and Quaternionic Vector Fields on Spheres”, Math. Notes, 93:1 (2013), 151–157  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Parton M., Piccinni P., “Spheres with More Than 7 Vector Fields: All the Fault of Spin(9)”, Linear Alg. Appl., 438:3 (2013), 1113–1131  crossref  mathscinet  zmath  isi  elib  scopus
    4. Rubin B., “Comparison of volumes of convex bodies in real, complex, and quaternionic spaces”, Adv. Math., 225:3 (2010), 1461–1498  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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