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Mat. Zametki, 2008, Volume 83, Issue 4, Pages 590–605 (Mi mz4578)  

This article is cited in 3 scientific papers (total in 3 papers)

Combinatorial Construction of Tangent Vector Fields on Spheres

A. A. Ohnikyan

Yerevan State University

Abstract: For every odd $n$, on the sphere $S^n$, $\rho(n)-1$ linear orthonormal tangent vector fields, where $\rho(n)$ is the Hurwitz–Radon number, are explicitly constructed. For each $8\times8$ 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

DOI: https://doi.org/10.4213/mzm4578

Full text: PDF file (533 kB)
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English version:
Mathematical Notes, 2008, 83:4, 539–553

Bibliographic databases:

UDC: 515.164.322
Received: 28.04.2006
Revised: 22.06.2007

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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\pages 590--605
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    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
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