The General Solutions of Frenet’s System in the Equiform Geometry of the Galilean, Pseudo-Galilean, Simple Isotropic

This paper is dedicated to Professor B. Pavković Abstract. 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 dif-ferent 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