Specialized Riemanian Spaces of the First Three Lacunaries by Groups of Isometric and Homothetic Motions
The article gives a classification of metrics of specialized Riemannian spaces, which carry four algebras at once in metrics Dm1 – real numbers, Cm2 – complex numbers, Hm3 – quaternions, Om4 – octions. Dimension of spaces n=m1+2m2+4m3+8m4 .The article presents a picture of lacunar spaces Vn4a also a...
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| Format: | Article |
| Language: | Russian |
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Educational institution «Belarusian State University of Informatics and Radioelectronics»
2023-06-01
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| Series: | Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki |
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| Online Access: | https://doklady.bsuir.by/jour/article/view/3654 |
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| _version_ | 1849398393200181248 |
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| author | Z. N. Chetyrkina |
| author_facet | Z. N. Chetyrkina |
| author_sort | Z. N. Chetyrkina |
| collection | DOAJ |
| description | The article gives a classification of metrics of specialized Riemannian spaces, which carry four algebras at once in metrics Dm1 – real numbers, Cm2 – complex numbers, Hm3 – quaternions, Om4 – octions. Dimension of spaces n=m1+2m2+4m3+8m4 .The article presents a picture of lacunar spaces Vn4a also a classification of metrics by groups of isometric Gr and homothetic Pr movements (r is the dimension of the group) is given. There are gaps in the orders r of these groups, which are called lacunae. Here are two lacunae and metrics of spaces Vn4a of the first three lacunarities in the image of I. P. Egorov. It is established that among the orders of r-groups of isometries Gr and homoteties Pr in specialized Riemann spaces Vn4a of the third lacunarity, there is one order r3max – 1, which is not feasible e. g. a punctate lacunarity was found. |
| format | Article |
| id | doaj-art-268829eb70204023a66dee41c8bc13b7 |
| institution | Kabale University |
| issn | 1729-7648 |
| language | Russian |
| publishDate | 2023-06-01 |
| publisher | Educational institution «Belarusian State University of Informatics and Radioelectronics» |
| record_format | Article |
| series | Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki |
| spelling | doaj-art-268829eb70204023a66dee41c8bc13b72025-08-20T03:38:38ZrusEducational institution «Belarusian State University of Informatics and Radioelectronics»Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki1729-76482023-06-012131111181912Specialized Riemanian Spaces of the First Three Lacunaries by Groups of Isometric and Homothetic MotionsZ. N. ChetyrkinaThe article gives a classification of metrics of specialized Riemannian spaces, which carry four algebras at once in metrics Dm1 – real numbers, Cm2 – complex numbers, Hm3 – quaternions, Om4 – octions. Dimension of spaces n=m1+2m2+4m3+8m4 .The article presents a picture of lacunar spaces Vn4a also a classification of metrics by groups of isometric Gr and homothetic Pr movements (r is the dimension of the group) is given. There are gaps in the orders r of these groups, which are called lacunae. Here are two lacunae and metrics of spaces Vn4a of the first three lacunarities in the image of I. P. Egorov. It is established that among the orders of r-groups of isometries Gr and homoteties Pr in specialized Riemann spaces Vn4a of the third lacunarity, there is one order r3max – 1, which is not feasible e. g. a punctate lacunarity was found.https://doklady.bsuir.by/jour/article/view/3654isometriehomotetiegroups of isometries and homotetiesorder of groupslacunaespaces of <i>k</i>-th lacunarity |
| spellingShingle | Z. N. Chetyrkina Specialized Riemanian Spaces of the First Three Lacunaries by Groups of Isometric and Homothetic Motions Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki isometrie homotetie groups of isometries and homoteties order of groups lacunae spaces of <i>k</i>-th lacunarity |
| title | Specialized Riemanian Spaces of the First Three Lacunaries by Groups of Isometric and Homothetic Motions |
| title_full | Specialized Riemanian Spaces of the First Three Lacunaries by Groups of Isometric and Homothetic Motions |
| title_fullStr | Specialized Riemanian Spaces of the First Three Lacunaries by Groups of Isometric and Homothetic Motions |
| title_full_unstemmed | Specialized Riemanian Spaces of the First Three Lacunaries by Groups of Isometric and Homothetic Motions |
| title_short | Specialized Riemanian Spaces of the First Three Lacunaries by Groups of Isometric and Homothetic Motions |
| title_sort | specialized riemanian spaces of the first three lacunaries by groups of isometric and homothetic motions |
| topic | isometrie homotetie groups of isometries and homoteties order of groups lacunae spaces of <i>k</i>-th lacunarity |
| url | https://doklady.bsuir.by/jour/article/view/3654 |
| work_keys_str_mv | AT znchetyrkina specializedriemanianspacesofthefirstthreelacunariesbygroupsofisometricandhomotheticmotions |