Pontryagin forms on homogeneous spaces (Q1074913)

It is known that the differential forms which represent characteristic classes carry extra geometric information beyond the topological (i.e. cohomological) information. The author shows how to compute the forms for a homogeneous space K/H, with K and H being compact Lie groups, in terms of roots of K and their projections into H. By this computational method he proves the following theorem: The homogeneous space SU(n)/SU(k) does not immerse isometrically in codimension less than 2 min([k/2],[(n- k)/2]).