Differential geometry of non-transversal intersection curves of three implicit hypersurfaces in Euclidean 4-space (Q738950)

The authors consider non-transversal intersection curves of three implicit hypersurfaces in Euclidean 4-space. The intersection is called non-transversal when the normal vectors are linearly dependent at the intersection point. In Euclidean 4-space, four kinds of intersection exist. Non-transversal intersections of three hypersurfaces with normal vectors \(N_i\) at the point \(p\) occur in two different cases, namely almost tangential intersection and tangential intersection, i.e., when the dimension of \(\mathrm{span}(N_1(p), N_2(p), N_3(p))\) equals 2 or 1, respectively. Here these two cases are discussed. Algorithms are given to find the Frenet vectors and the curvature of the non-transversal intersection curves. At the end, the authors give several interesting special examples.