Self-conjugate vectors of immersed 3-manifolds in

This paper generalizes the notion of asymptotic vectors, parabolic curves, and inflection points on surfaces in R 4 to n-manifolds in R 2 n . Because the dimension and codimension are the same in both cases, most of the interesting properties of these objects still exist when we move to the higher dimension. In particular, we study in detail the case of 3-manifolds immersed in R 6 . We classify the possible generic algebraic structures of the asymptotic vectors at a parabolic point or an inflection point, and we classify the generic topological structures of the parabolic surface.