Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki (Jun 2024)

On Gaps in the Orders of Complete Groups of Isometry and Homoteties in Specialized Riemannian Spaces and Metrics of the Most Mobile of These Spaces of the First Six Lacunars

  • Z. N. Chetyrkina

Journal volume & issue
Vol. 22, no. 3
pp. 106 – 111

Abstract

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In the present paper there are considered metric Riemannian spaces Vn4a, in the metrics of which four algebraic structures work at once: real numbers Dm1 and complex numbers Cm2, quaternions Hm3 and octions Om4. We are interested in these spaces in terms of their isometric and homothetic mobility. It turns out that there are lacunas (gaps) in the orders r of complete groups of isometries Gr and homotheties Pr. The metrics of the most mobile spaces Vn4a of the first six lacunarities in the sense of I. P. Egorov are found.

Keywords