I am working on a problem that requires me to compute curl(V) div(V) where V: R4 -> R3, (coordinates are (t,x,y,z) - where x,y,z are time dependent variable) and basis of V =[Vx Vy Vz].

I know I can get curl(V) by taking differential of 1-form and div(V) by taking differential of 2-form.

In this case, is 1-form can be written as Vxdx + Vydy + Vzdz or 

Vxdx + Vxdt + Vydy + Vydt + Vzdz + Vzdt? 

Similarly, is 2-form can be written as Vxdy ∧ dz + Vydz ∧ dx + Vzdx ∧ dy or 

Vxdy ∧ dz + Vxdy ∧ dt+ Vxdt ∧ dz + Vydz ∧ dx + Vydz ∧ dt + Vydz ∧ dt + Vzdx ∧ dy + Vzdt ∧ dy +Vzdx ∧ dt??