Examination of the geodesic curvatures and geodesic torsions of the transversal intersection curve in E^n

Abstract

This study aims to compute all geodesic curvatures and geodesic torsions of an implicit curve in Euclidean n-space. Since
an implicit curve is determined by the intersection of (n − 1) implicit hypersurfaces in E^n, the results obtained in this paper complete
the lacking curvatures for a transversal intersection curve. As a result, the approach proposed in the paper can be viewed as a partial
solution to the open problem that Goldman identified in 2005. An algorithm has been proposed to handle the difficulty of calculating
geodesic curvatures and geodesic torsions in spaces of higher dimensions. Then, an computational algorithms produced by MATLAB
are utilized to display the outcomes in the form of illustrative examples.