Differential geometry of transversal intersection curves of hypersurfaces in ℝ5

Abstract In this paper, we present the algorithms for calculating the differential geometric quantities {t, n, b1, b2, b3, k2, k3, k4}, geodesic curvature and geodesic torsion of the transversal intersection curve of four hypersurfaces (given by parametric representation) in Euclidean space ℝ5. In transversal intersection, the normals of the surfaces at the intersection point are linearly independent, while as in nontransversal intersection, the normals of the surfaces at the intersection point axe linearly dependent.