This article is cited in 3 papers

Geometry and topology

Analytic embedding of some two-dimensional geometries of maximal mobility

V. A. Kyrov

Gorno-Altaiisk State University, 1, Lenkina str., Gorno-Altaisk, 649000, Russia

Abstract: In this paper, we solve the problem of embedding two-dimensional geometries: simplicial, dual-gelmgoltz, Helmholtz proper and pseudohelmholtz, into three-dimensional geometries. This problem is solved by an analytical method. The functions defining these geometries are found. Basic operators of Lie algebras of groups of motions are calculated.

Keywords: geometry of maximum mobility, Lie transformation group, functional equation, differential equation, Lie algebra.

UDC: 514.1,517.912

MSC: 53D05, 39B22

Received August 26, 2018, published June 28, 2019

DOI: 10.33048/semi.2019.16.061

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