# Math Help - vector field on surface

1. ## vector field on surface

The question is :
Prove that an orientable compact surface in R^3 has a differentiable vector field without singular points iff S is homeomorphic to a torus

I have proved one direction by using Poincare's theorem ,but I can't prove that if S is homemorphic to a torus then it has a vector field without singular points,please help.

2. If the torus is obtained from the unit square by identifying opposite edges, then you can use any constant (nonzero) vector field on the square.