Curvature computations for the intersection curves of hypersurfaces in Euclidean n-space

Abstract

The aim of this paper is to derive the curvatures and Frenet vectors of the intersection curve of (n - 1) transversally intersecting hypersurfaces represented either in implicit or in parametric form in Euclidean n-space. Since the intersection of (n - 1) implicit hypersurfaces defines an implicit curve in n-dimensions, the method derived for the implicit case can be considered as a partial answer to the open problem posed by Ron Goldman in 2005. Also, an application is provided for the implicit case where the results are presented by using computer codes currently produced in MATLAB. (C) 2020 Elsevier B.V. All rights reserved.