ERGIN BAYRAM 1 AND EMIN KASAP 2 1. Ondokuz Mayıs University, Faculty of Arts and Sciences,
Mathematics Department, Atakum, Samsun, 55139, TURKEY, e-mail: erginbay-ram@yahoo.com
2. Ondokuz Mayıs University, Faculty of Arts and Sciences,
Mathematics Department, Atakum, Samsun, 55139, TURKEY,
e-mail: kasape@omu.edu.tr
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 analyze the necessary and sufficient conditions for that curve to be geodesic. We illustrate this method by presenting some examples.
