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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 916–937 (Mi semr1103)  

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.

DOI: https://doi.org/10.33048/semi.2019.16.061

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Bibliographic databases:

UDC: 514.1,517.912
MSC: 53D05, 39B22
Received August 26, 2018, published June 28, 2019

Citation: V. A. Kyrov, “Analytic embedding of some two-dimensional geometries of maximal mobility”, Sib. Èlektron. Mat. Izv., 16 (2019), 916–937

Citation in format AMSBIB
\Bibitem{Kyr19}
\by V.~A.~Kyrov
\paper Analytic embedding of some two-dimensional geometries of maximal mobility
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 916--937
\mathnet{http://mi.mathnet.ru/semr1103}
\crossref{https://doi.org/10.33048/semi.2019.16.061}


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