In this work, first, we express some characterizations of helices and ccr curves in the Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of a helix are presented. Moreover, in the same space, some new characterizations of involute of a helix are presented.

The Riemannian geometry of elastica in one and two dimensions is considered. Two examples from engineering science are given. The first is the deflexion or Frenet curvature of the elastic filament rod where the Riemannian curvature vanishes, since the curve is one dimensional. However the Frenet curvature scalar appears on the LeviCivita-Christoffel symbol of the Riemannian geometry. A second e...

In this paper the equiform differential geometry of curves in the pseudo-Galilean space G3 is introduced. Basic invariants and a moving trihedron are described. Frenet formulas are derived and the fundamental theorem of curves in equiform geometry of G3 is proved. The curves of constant curvatures are described.