In the present study, we derive the problem of constructing a hypersurface family from a given isogeodesic curve in the 4D Galilean space $\mathbf{ G}_{ 4}.$ We obtain the hypersurface as a linear combination of the Frenet frame in $\mathbf{ G}_{ 4}$ and examine the necessary and sufficient conditions for the curve as a geodesic curve$.$ Finally, some examples related to our method are given for the sake of clarity.
Categories: math.GM