4
$\begingroup$

I came across this exercise in Warner's Foundations of Differential Manifolds and Lie Groups,

Let $N \in M$ be a submanifold. Let $\gamma \colon (a,b) \to M$ be a $C^{\infty}$ curve such that $\gamma(a,b) \subset N$. Show that it is not necessarily true that $\dot \gamma (t) \in N_{\gamma (t)}$ for each $t \in (a,b)$.

I'm having trouble trying to find an example of such a curve. Could someone give me an example or show me the way? Either way thanks!

  • 0
    all right, thanks @GeorgesElencwajg! I can see the trick now, it wasn´t hard after all... I feel a little ashamed now, but relief. Thanks so much guys!2012-07-11

0 Answers 0