Is f_m Smooth When f Is a Smooth Map Between Manifolds?

[slevvio]

Hello everyone, I just had a quick question I was hoping somebody could answer.

If f: M \times N \rightarrow P is a smooth map, where M,N and P are smooth manifolds, then is it true for fixed m that f_m : N \rightarrow P is smooth, where f_m (n) = f(m,n)?

Any help would be appreciated.

 

[quasar987]

Of course, since the equivalent statement when M=R^m, N=R^n is true.

 

[slevvio]

ok thank you!