Abstract
In this paper, we study the problem of finding a hypersurface family from a given spatial geodesic curve in R<sup>4</sup>. 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 analyze the necessary and sufficient conditions for that curve to be geodesic. We illustrate this method by presenting some examples.
Cuvinte cheie
hypersurface
Frenet frame
geodesic