Hello,

Let M be a manifold and j:M->$\displaystyle \mathbb{R}^n$ a smooth embedding.

What is the local structure of dj?

If we have such a embedding, then dj:TM->$\displaystyle T\mathbb{R}^n$ is a map between the Tangent bundles. But what about the local structure?

I have found this equation, but i'm not sure, whether it is true in general or not:

$\displaystyle dj(p)[f]=\sum_{i=1}^n X^j \frac{d}{dx_i}_{|p}$, with $\displaystyle <x,X^j>=0$

Thanks in advance!