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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2019 • Question 3

Question

Math 6510 • Differentiable Manifolds Spring 2019 • Question 3

Let \(\alpha =y\,dx-x\,dy+dz\) be a one form on \(\mathbb {R}^3\). Define a 2-plane field distribution at \(p\in \mathbb {R}^3\) by \(\Delta _p=\{V\in T_p\mathbb {R}^3:\alpha (V)=0\}\). Is the plane field \(\Delta _p\) integrable? Why?

Raw LaTeX

Let \(\alpha=y\,dx-x\,dy+dz\) be a one form on \(\R^3\). Define a 2-plane field
distribution at \(p\in\R^3\) by
\(\Delta_p=\{V\in T_p\R^3:\alpha(V)=0\}\). Is the plane field \(\Delta_p\)
integrable? Why?

Topic Tags

Distributions, Plane Fields, and Frobenius Integrability