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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 The General Solutions of Frenet's System in the Equiform Geometry of the Galilean, Pseudo-Galilean, Simple Isotropic and Double Isotropic Space // International Mathematical Forum, 6 (2011), 17; 837-856

Podaci o odgovornosti

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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Podaci o izdanju

6 (17)

2011.

837-856

objavljeno

1312-7594

1314-7536

Povezanost rada

Matematika