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

摘要

The aim of this paper is to obtain all Frenet apparatus of transversal intersection curves by giving new and easy applicable methods in three and four-dimensional Euclidean spaces. The methods includes a few operator which are obtained by using the idea of Willmore. By using these operators we obtain the Frenet vectors and curvatures of the transversal intersection curves of two (three) surfaces (hypersurfaces) in which at least one (hyper)surface is given parametrically.