You can just consider the example of a smooth coordinate chart for , and focus on as the manifold in question.
At , if and for , we will have
Let M be a manifold and j:M-> a smooth embedding.
What is the local structure of dj?
If we have such a embedding, then dj:TM-> 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:
Thanks in advance!