Yes, Lie derivative is a good approach.  For future reference, the command DGscalar("form", f) is used to represent a function f as a differential form of zero degree.

charlie

Maple 15 seems to work ok with Lion. I am running the latest versions of each. There are a few glitches, but not that many more than usual.

charlie

If I were in this situation, I would solve the equations defining the map i: S -> M for the coordinates of S in terms of those of M. If (x, y, z) are coordintes on M and (u,v) are coordinates on S, this transformation would have equations of the form [u=u(x,y,z), v=v(x,y,z)].  Define this as a another DifferentialGeometry transformation. Use this second transformation in the PushForward command as the second argument (the first argument being the map i). This should give you vector fields on M you can differentiate.

See Example 7 in the help page and see also "PullbackVector".

Does this help?

Charlie Torre