This talk is about the mutually orthogonal one dimensional singular foliations with singularities, in oriented n dimensional manifolds $\M^n$, whose leaves are the integral curves of the principal curvature direction fields associated to immersions $\alpha:\M^n\rightarrow \R^{n+1}$. We focus on behavior of these foliations around singularities defined by the points where at least two principal curvature coincide.