In this paper, we define the curve

Klein pronounced a different definition of geometry in his introductory speech at the University of Erlangen in 1872. He explained that geometry, given by a subgroup

One of the important research areas in differential geometry is the theory of curves examined in various spaces. In particular, it has been examined in a lot of papers and remarkable results have been obtained in the 3-dimensional Galilean space [

The notion of the curves at a constant distance from the edge of regression has been introduced by Vogler. He has studied the curves traced on a torse at a constant distance from its edge of regression. The torse of a space curve in

This subject has been studied in Euclidean 3-space since the 1970s, and it is a method that generates a new curve from the curve through the Frenet frame of the curve. For the first time, we will discuss this issue in 3-dimensional Galilean space. While the curve is produced by using the unit vector which is defined by the Frenet frame apparatus of a curve in Euclidean 3-space, we will have produced the curve by considering two situations in the Galilean 3-space. This is because, in Galilean space, vectors are treated in two ways, isotropic and non-isotropic.

In this paper, we first recall the essential preliminaries on the Galilean 3-space. Then, we define curves in the Galilean 3-space and give the curvature properties of these curves. In the main part of our study, we define a curve noted by

Let us consider a curve

The Galilean space

Now, let us consider the basic definitions and notions.

Let

If

Let

The Galilean vector product of two vectors in

A vector

If the vectors

If the vectors

Let

Let

In this case, the functions

Then,

The using

If we take the derivation of

And from

Using

As a consequence, the unit binormal vector

Now, let us construct the Frenet frame of

If we take the norm of two sides of

Using

In these calculations we used

In this case, we have

If we take the norm of two sides of

In these calculations, we use

In this case, we have

The ruled surfaces in

A ruled surface of type

Additionally, the parameter of distribution

We know that if

If we take

Now, we consider that

Finally considering

Similarly to

Thus, the following theorem can be written:

We take as

Hence,

The Frenet frame fields of the curve of

Considering

In

In

In this study, we present a method that generates a new curve from the curve using the Frenet frame of a curve that is parameterized by arc length in

The authors wish to express their appreciation to the reviewers for their helpful suggestions which greatly improved the presentation of this paper.