given a vector bundle $V \rightarrow N$ over a manifold $N$ and let's assume $N \hookrightarrow M$ is embedded into a manifold $M$ is there a way to extend $V$ to a bundle over $M$, i.e. is there a bundle $\tilde V \rightarrow M$ such that $\tilde VN=V$. I hardly believe that this is true in general, e.g. if I look at $S^2 \hookrightarrow \mathbb{R}^3$ and its tangent bundle it seems to me, that there is no way how to extend $TS^2$ continously but are there criterions. Of course, if the bundle is trivial the answer is yes...
