On the Lusternik–Schnirelmann category of Stiefel manifolds

We determine the Lusternik–Schnirelmann category of real Stiefel manifolds V n , k and quaternionic Stiefel manifolds X n , k for n ⩾ 2 k which is equal to the cup-length of the mod 2 cohomology of V n , k and the integer cohomology of X n , k , respectively.