Asymptotic curves of submanifolds (Q1324895)

It is known that the torsion of asymptotic lines on a surface in Euclidean space \(E^3\) is equal to \(\pm \sqrt {-K}\), where \(K\) is the Gaussian curvature. The author generalizes this theorem to the case of higher-dimensional submanifolds in a Riemannian space. He computes different curvatures of asymptotic lines through sectional curvatures of the submanifold, the ambient space and the angle between the normal space of the submanifold and vectors of the natural frame of the curve.