3. [4 points] Let X be a vector field on Rm such that for every p = Rm the maximal

integral curve of X going through p at time zero is defined on the whole of R.

Consider the stereographic projection : Sm - {N} → Rm, where N denotes the

North Pole. Let Y be a vector field on the sphere Sm such that its restriction to

Sm{N} equals (0-¹),X.

What can you say about YN, the value of Y at the North Pole?