Osculating hyperplanes and asymptotic directions of codimension two submanifolds of Euclidean spaces (Q1125240)

In this interesting paper, the authors define the binormal and the asymptotic directions for submanifolds embedded with codimension 2 into Euclidean spaces. Necessary conditions are obtained, in terms of the existence of such directions, for the convexity and the sphericity of these submanifolds.