HelpA problem about embedded surface.

[aquarius]

I have a parametrization of a torus T^2:t(u,v)=((2+cosu)cosv,(2+cosu)sinv,sinu). How to show that T^2 is an embedded surface in R^3? How to show that the tangent bundleT(T^2) is trivial? Thanks.

 

[zhentil]

There's only one way to show that's it's an embedded surface. Show it's a 1-1 immersion, and note that the torus is compact.