|
This article is cited in 4 scientific papers (total in 4 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.
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
Linking options:
https://www.mathnet.ru/eng/vuu567 https://www.mathnet.ru/eng/vuu/v27/i1/p42
|
Statistics & downloads: |
Abstract page: | 397 | Full-text PDF : | 155 | References: | 36 |
|