An Approach for Hypersurface Family with Common Geodesic Curve in the 4D Galilean Space G4

Abstract

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.