Generic Singularities of H-Directions *

On immersed surfaces in R ⁴ we can consider the H-lines, which are characterized by the condition that their tangent lines are carried over the directions of the mean curvature vector field. We call the singularities of these lines H-singularities. In this paper we analyze the H-singularities and we show that their generic local configurations are analogous to Darbouxian umbilic points on surfaces immersed in R ³.