Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2009 • Question 5

Question

Math 6510 • Differentiable Manifolds Fall 2009 • Question 5

  1. State Stokes’ Theorem.
  2. Given two 3-forms on \(S^7\), denoted \(\theta \) and \(\omega \), prove that \[ \int _{S^7}d\theta \wedge \omega =\int _{S^7}\theta \wedge d\omega . \]

Raw LaTeX

\begin{enumerate}
\item[(a)] State Stokes' Theorem.
\item[(b)] Given two 3-forms on \(S^7\), denoted \(\theta\) and \(\omega\), prove that
\[
  \int_{S^7}d\theta\wedge\omega=\int_{S^7}\theta\wedge d\omega.
\]
\end{enumerate}

Topic Tags

Compactly Supported Forms and Integration Differential Forms and Exterior Calculus Stokes' Theorem and Integration on Manifolds