Inflectional loci of scrolls overs smooth, projective varieties

Let X \subset P^N be a scroll over a an m-dimensional variety Y. We find the locally free sheaves on X governing the osculating behaviour of X, and, under certain assumptions, we compute the cohomology class and the degree of the inflectional locus of X. The case m=1 was treaded in a previous paper. Here we treat the case m > 1, which is more complicated for at least two reasons: the expression for the osculating sheaves and the computations of the class of the inflectional locus become more complex, and the dimension requirements needed to ensure validity of the formulas are more severe.