Stable extendibility of some complex vector bundles over lens spaces and Schwarzenberger's theorem

We obtain conditions for stable extendibility of some complex vector bundles over the (2n+1) dimensional standard lens space L-n(p) mod p, where p is a prime. Furthermore, we study stable extendibility of the bundle pi(n)* (tau(CPn)) induced by the natural projection pi(n) : L-n (p) -> CPn from the complex tangent bundle tau(CPn) of the complex projective n-space CPn. As an application, we have a result on stable extendibility of tau(CPn) which gives another proof of Schwarzenberger's theorem.