L–S categories of vector bundles over projective spaces

I.M. James calculated vecat ( k γ R ) , the L–S category of k γ R , for k = 2 t and γ R , the canonical line bundle over the ( 2 t − 1 ) -dimensional real projective space. In this paper, we calculate vecat ( k γ R ) for integers k and γ R , the canonical line bundle over projective spaces. We also calculate vecat F ξ , the L–S category of ξ as an F -vector bundle, where F = R or C , for ξ, multiple Whitney sums of canonical line bundles over complex and quaternion projective spaces.