Geodesic
Coordinate-free recording
Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 4, pp. 412-418

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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. 
@article{CHFMJ_2019_4_4_a3,
     author = {G. G. Mikhailichenko and A. A. Simonov},
     title = {Coordinate-free recording},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {412--418},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_4_a3/}
}
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G. G. Mikhailichenko; A. A. Simonov. Coordinate-free recording. Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 4, pp. 412-418. http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_4_a3/