Lines of curvature near umbilical points on surfaces immersed in \(\mathbb{R}^ 4\)
The authors study the principal configurations (the set formed by umbilical points and families of lines of maximal and minimal curvatures) of pairs consisting of an immersion of a compact orientable surface in a 4-space and a smooth unitary vector field normal to the immersed surface. They prove a genericity theorem for certain types of pairs which are defined by the Darboux conditions at umbilical points.
scientific article; zbMATH DE number 780911