Coordinate-free recording of helmholtz planes

G. G. Mikhailichenko, A. A. Simonov

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)412-418
Number of pages7
JournalChelyabinsk Physical and Mathematical Journal
Issue number4
Publication statusPublished - 1 Jan 2019


  • Geometry of maximum mobility
  • Group of transformations
  • Helmholtz planes
  • Metric function
  • Two-dimensional geometries


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