Willmore-like methods for the intersection curve of parametric (hyper) surfaces

This study consists of seven sections. The aim of thesis and review of the literature are given in the first chapter. In the second chapter, some basic concepts related to differential geometry of curves and surfaces are indicated. In the third chapter, the Willmore method which shows how to calculate the curvature and torsion of the intersection curve of two surfaces given by their implicit equations is explained and in the fourth chapter, the extension of this method into four-dimensional space is mentioned. The fifth and the sixth sections are the original part of thesis. In the fifth chapter, the calculation of Frenet apparatus of the transversal intersection curve of two surfaces in which at least one surface is given by parametrically in 3-dimensional Euclidian space is shown by using the idea of Willmore?s method. In the sixth chapter, with Willmore-like methods, how we can calculate the Frenet apparatus of the transversal intersecion curve of three hypersurfaces in which at least one is given by its parametric equation in 4-dimensional Euclidean space is expressed. In the seventh chapter, conclusions and recommendations are presented.