  In this paper, we study the problem of finding a hypersurface family from a
given spatial geodesic curve in R4. We obtain the parametric representation for
a hypersurface family whose members have the same curve as a given geodesic
curve. Using the Frenet frame of the given geodesic curve, we present the
hypersurface as a linear combination of this frame and analyse the necessary
and sufficient condition for that curve to be geodesic. We illustrate this
method by presenting some examples.
