Umbilic Singularities and Lines of Curvature on Ellipsoids of ${\mathbb   R}^4$
  The topological structure of the lines of principal curvature, the umbilic and partially umbilic singularities of all tridimensional ellipsoids of ${\mathbb R}^4$ is described. 
D\'ebora Lopes, Jorge Sotomayor and Ronaldo Garcia
math.DS math.DG