Mathematics

Coordinate-free recording of Helmholtz planes

G. G. Mikhailichenko^a, A. A. Simonov<sup>b

a</sup> Gorno-Altaisk State University, Gorno-Altaisk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: The metrics of most geometries of maximum mobility can be written in the coordinateless form. In this paper, we consider some Helmholtz planes, which are geometries of maximum local mobility, whose coordinateless recording was unknown. Implicitly defined functions are found to construct such a record.

Keywords: two-dimensional geometries, geometry of maximum mobility, group of transformations, Helmholtz planes, metric function.

UDC: 514.1

Received: 08.06.2019
Revised: 08.10.2019

DOI: 10.24411/2500-0101-2019-14404

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