L-S categories of vector bundles over projective spaces

I.M. James calculated vecat(kγR), the L-S category of kγR, for k=2t and γR, the canonical line bundle over the (2t−1)-dimensional real projective space. In this paper, we calculate vecat(kγR) for integers k and γR, the canonical line bundle over projective spaces. We also calculate vecatFξ, 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.