Parametric Representation of a Hypersurface Family With a Common Spatial Geodesic

Abstract

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.

17 pages, 3 figures