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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2021 • Question 4

Question

Math 6510 • Differentiable Manifolds Spring 2021 • Question 4

Let \(f:\mathbb {R}^3\to \mathbb {R}^2\) be the function \(f(x,y,z)=(xy,z)\) and let \(\omega =dx\wedge dy\) be the area form on \(\mathbb {R}^2\). Compute the pull-back \(f^*(\omega )\).

Raw LaTeX

Let \(f:\mathbb{R}^3\to\mathbb{R}^2\) be the function \(f(x,y,z)=(xy,z)\) and let \(\omega=dx\wedge dy\)
be the area form on \(\mathbb{R}^2\). Compute the pull-back \(f^*(\omega)\).

Topic Tags

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