Formulas for second curvature, third curvature, normal curvature, first geodesic curvature and first geodesic torsion of implicit curve in n-dimensions

Abstract

We present closed formulas for computing the differential geometry properties of the intersection curve of n−1 implicit hypersurfaces in Rn. These closed formulas include second curvature, third curvature, normal curvature, first geodesic curvature and first geodesic torsion for implicit curves in n-dimensions.