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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2002 • Question 9

Question

Math 6510 • Differentiable Manifolds Fall 2002 • Question 9

Compute the pull-back of the differential form \[ \omega =x\,dx\wedge dy+z\,dy\wedge dz \] in \(\mathbb {R}^3\) under the map \(f:\mathbb {R}^2\to \mathbb {R}^3\) given by \[ f(u,v)=(u^2,u+v,\sin (u+v)). \]

Raw LaTeX

Compute the pull-back of the differential form
\[
  \omega=x\,dx\wedge dy+z\,dy\wedge dz
\]
in \(\mathbb{R}^3\) under the map \(f:\mathbb{R}^2\to\mathbb{R}^3\) given by
\[
  f(u,v)=(u^2,u+v,\sin(u+v)).
\]

Topic Tags

Differential Forms and Exterior Calculus Pullbacks and Wedge Products Tangent Spaces and Differential Maps