Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2019 • Question 4

Question

Math 6510 • Differentiable Manifolds Fall 2019 • Question 4

Let \(M^m\) be a smooth compact orientable manifold and \(\omega \in \Omega ^m(M)\) a smooth, nonvanishing \(m\)-form that determines the orientation of \(M\). Show that \(\int _M\omega >0\).

Raw LaTeX

Let \(M^m\) be a smooth compact orientable manifold and
\(\omega\in\Omega^m(M)\) a smooth, nonvanishing \(m\)-form that determines the
orientation of \(M\). Show that \(\int_M\omega>0\).

Topic Tags

Differential Forms and Exterior Calculus Homotopy and Degree on Manifolds Orientability and Volume Forms Smooth Manifolds and Embedded Submanifolds