1. The problem statement, all variables and given/known data Let w be the form w= xdydz in R^3. Let S^2 be the unit sphere in R^3. If we restrict w on S^2, is w exact? 2. Relevant equations 3. The attempt at a solution My guess is w is not exact on S^2. Suppose w is exact on S^2. Then w=da for some 1-form a=fdx+gdy+hdz. Then by definition of exterior derivative, we get w=(-df/dy+dg/dx)(dx^dy)+(-df/dz+dh/dx)(dx^dz)+(-dg/dz+dh/dy)(dy^dz) So we get the conditions: df/dy=dg/dx, df/dz=dh/dx, x=-dg/dz+dh/dy. I think I should use a fact that I am working on a unit sphere. Could anybody help me?