In this paper, we analyze the geometric structure of a Euclidean submanifold whose osculating spaces form a nonconstant family of proper subspaces of the same dimension. We prove that if the rate of change of the osculating spaces is small, then the submanifold must be a (submanifold of a) ruled submanifold of a very special type. We also give a sharp estimate of the dimension of the rulings.
Marcos Dajczer. Ruy Tojeiro. "Submanifolds with nonparallel first normal bundle revisited." Publ. Mat. 58 (1) 179 - 191, 2014.