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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 1, Pages 42–53 (Mi vuu567)  

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

MATHEMATICS

Embedding of phenomenologically symmetric geometries of two sets of rank $(N,M)$ into phenomenologically symmetric geometries of two sets of rank $(N+1,M)$

V. A. Kyrov

Gorno-Altaisk State University, ul. Lenkina, 1, Gorno-Altaisk, 649000, Russia

Abstract: In this paper, a classification of phenomenologically symmetric geometries of two sets of rank $(n+1,m)$ with $n\geqslant 2$ and $m\geqslant 3$ is constructed by the method of embedding. The essence of this method is to find the metric functions of phenomenologically symmetric geometries of two high-rank sets by the known phenomenologically symmetric geometries of two sets of a rank which is lower by unity. By the known metric function of the phenomenologically symmetric geometry of two sets of rank $(n+1,n)$, we find the metric function of the phenomenologically symmetric geometry of rank $(n+1,n+1)$, on the basis of which we find later the metric function of the phenomenologically symmetric geometry of rank $(n+1,n+2)$. Then we prove that there is no embedding of the phenomenologically symmetric geometry of two sets of rank $(n+1,n+2)$ in the phenomenologically symmetric geometry of two sets of rank $(n+1,n+3)$. At the end of the paper, we complete the classification using the mathematical induction method and taking account of the symmetry of a metric function with respect to the first and the second argument. To solve the problem, we write special functional equations, which reduce to the well-known differential equations.

Keywords: phenomenologically symmetric geometry of two sets, metric function, differential equation.

DOI: https://doi.org/10.20537/vm170104

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Bibliographic databases:

UDC: 517.912, 514.1
MSC: 35F05, 39B05, 51P99
Received: 31.10.2016

Citation: V. A. Kyrov, “Embedding of phenomenologically symmetric geometries of two sets of rank $(N,M)$ into phenomenologically symmetric geometries of two sets of rank $(N+1,M)$”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:1 (2017), 42–53

Citation in format AMSBIB
\Bibitem{Kyr17}
\by V.~A.~Kyrov
\paper Embedding of phenomenologically symmetric geometries of two sets of rank $(N,M)$ into phenomenologically symmetric geometries of two sets of rank $(N+1,M)$
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 1
\pages 42--53
\mathnet{http://mi.mathnet.ru/vuu567}
\crossref{https://doi.org/10.20537/vm170104}
\elib{http://elibrary.ru/item.asp?id=28808554}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Kyrov, “Analiticheskii metod vlozheniya mnogomernykh psevdoevklidovykh geometrii”, Sib. elektron. matem. izv., 15 (2018), 741–758  mathnet  crossref
    2. V. A. Kyrov, G. G. Mikhailichenko, “Vlozhenie additivnoi dvumetricheskoi fenomenologicheski simmetrichnoi geometrii dvukh mnozhestv ranga $(2,2)$ v dvumetricheskie fenomenologicheski simmetrichnye geometrii dvukh mnozhestv ranga $(3,2)$”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:3 (2018), 305–327  mathnet  crossref  elib
    3. V. A. Kyrov, “Analiticheskoe vlozhenie nekotorykh dvumernykh geometrii maksimalnoi podvizhnosti”, Sib. elektron. matem. izv., 16 (2019), 916–937  mathnet  crossref
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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