Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2005 • Question 5

Question

Math 6510 • Differentiable Manifolds Fall 2005 • Question 5

Let \(f:\mathbb {R}^2\to \mathbb {R}^3\) be the function given by \(f(x,y)=(x^2-y,x+y^2,\sin (x))\). Let \(\omega \) be the 2-form on \(\mathbb {R}^3\) given by \(\omega (u,v,w)=u\,dv\wedge dw\). Compute the pull-back \(f^*\omega \).

Raw LaTeX

Let \(f:\mathbb{R}^2\to\mathbb{R}^3\) be the function given by
\(f(x,y)=(x^2-y,x+y^2,\sin(x))\). Let \(\omega\) be the 2-form on \(\mathbb{R}^3\) given by
\(\omega(u,v,w)=u\,dv\wedge dw\). Compute the pull-back \(f^*\omega\).

Topic Tags

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