Semiparallel submanifolds with plane generators of codimension two in a Euclidean space (Q2784826)

A submanifold generated by plane leaves of codimension two in a Euclidean space is, in general, intrinsically a Riemannian manifold of conullity two. The main result: If such a manifold is semiparallel (i.e. \(\overline{R}(X,Y) \cdot h = 0\), \(\overline{R}\) = curvature tensor of the van der Waerden-Bortolotti connection, \(h\) = second fundamental form) and intrinsically of conullity two (i.e. \(R(X,Y) \cdot R = 0\), \(R\) = curvature tensor), then it is of planar type, i.e. it has infinitely many real intrinsically asymptotic distributions.