The General Solutions of Frenet's System in the Equiform Geometry of the Galilean, Pseudo-Galilean, Simple Isotropic and Double Isotropic Space (CROSBI ID 171475)
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Erjavec, Zlatko ; Divjak, Blaženka ; Horvat, Damir
engleski
The General Solutions of Frenet's System in the Equiform Geometry of the Galilean, Pseudo-Galilean, Simple Isotropic and Double Isotropic Space
In this paper several Cayley-Klein geometries and associated equiform geometries are described. Equiform geometry of Cayley-Klein space is obtained by requesting that similarity group of the space preserves angles between planes and lines, respectively. Further, invariants of curves in different equiform geometries are introduced. Then, the general solutions of Frenet's system in the equiform geometry of the Galilean, pseudo-Galilean, simple isotropic and double isotropic space are given. The generalizations of given solutions to the sequences of functions are considered, as well.
equiform geometry; Galilean space; pseudo-Galilean space; simple isotropic space; double isotropic space; Frenet's system
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