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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2010 • Question 3

Question

Math 6510 • Differentiable Manifolds Spring 2010 • Question 3

Find \(a,b\in C^\infty (\mathbb {R}^3)\) such that \[ d(xyz\,dx\wedge dy+3x^3\,dy\wedge dz)=a\,dx\wedge dy\wedge dz \] and \[ dx\wedge (14x\,dz)\wedge dy=b\,dx\wedge dy\wedge dz. \]

Raw LaTeX

Find \(a,b\in C^\infty(\R^3)\) such that
\[
  d(xyz\,dx\wedge dy+3x^3\,dy\wedge dz)=a\,dx\wedge dy\wedge dz
\]
and
\[
  dx\wedge(14x\,dz)\wedge dy=b\,dx\wedge dy\wedge dz.
\]

Topic Tags

Differential Forms and Exterior Calculus