Abstract
For every odd n, on the sphere S n, 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.
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Original Russian Text © A. A. Ognikyan, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 4, pp. 590–605.
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Ognikyan, A.A. Combinatorial construction of tangent vector fields on spheres. Math Notes 83, 539–553 (2008). https://doi.org/10.1134/S0001434608030279
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DOI: https://doi.org/10.1134/S0001434608030279