Compute the pullback \(f^*\omega \) of the differential form \[ \omega =dx\wedge dy \] by the map \(f:\mathbb {R}^3\to \mathbb {R}^3\), \(f(x,y,z)=(xyz,y+x,z)\).
Question
Math 6510 • Differentiable Manifolds
Fall 2001 • Question 10
Question
Fall 2001 • Question 10
Compute the pullback \(f^*\omega \) of the differential form \[ \omega =dx\wedge dy \] by the map \(f:\mathbb {R}^3\to \mathbb {R}^3\), \(f(x,y,z)=(xyz,y+x,z)\).