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Explicitly construct a differentiable vector field $W$ in the torus.

Meridians of $T^2$ parameterized by arc length, for all $p \in T^2$, define $W (p)$ as the velocity vector of the meridian passing through $p$.

Maybe could help

$x=(R+r \cos \phi)\cos \theta$;

$y=(R+r \cos \phi)\sin \theta$;

$z=r \sin \phi$

Where $\theta, \phi \in [0, 2\pi[$ Thanks

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up vote 1 down vote accepted

I guess that the second question is actually a part of the exercise. Hint: the variable that parametrizes each meridian is $\phi$. Hence, the velocity vector of the meridian is the partial derivative with respect to $\phi$.

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