Hypersurface families with common non-null geodesic in Minkowski 4-space

Abstract

In this study, we create hypersurface families from each non-null isogeodesic, with non-null Frenet vectors, given in the Minkowski 4-space. We obtain parametric representations for hypersurface families whose members have the same curves as the given isogeodesic curves. By using the Frenet frame of each given geodesic curve, we create the hypersurfaces as a linear combination of this Frenet frame and obtain the necessary and sufficient conditions for these curves to be isogeodesic. Also, we give some examples so that the method presented is clear and understandable. In addition, the graphs of the surfaces formed by projecting the surfaces given with parametric equations to 3-dimensional space are drawn.