On Stiefel-Whitney classes of vector bundles over real Stiefel Manifolds

Abstract

In this article we show that there are at most two integers up to 2(n − k), which can occur as the degrees of nonzero Stiefel-Whitney classes of vector bundles over the Stiefel manifold V k (R n ). In the case when n > k(k + 4)/4, we show that if w 2 q (ξ) is the first nonzero Stiefel-Whitney class of a vector bundle ξ over V k (R n ) then w t (ξ) is zero if t is not a multiple of 2 q . In addition, we give relations among Stiefel-Whitney classes whose degrees are multiples of 2 q .