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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2016 • Question 3

Question

Math 6510 • Differentiable Manifolds Fall 2016 • Question 3

For any \(p\in \mathbb {R}^3\), let \(K_p\) be the kernel of the form \(2dz-3y\,dx\) taken at the point \(p\). Then \(K_p\) defines a plane field on the manifold \(\mathbb {R}^3\). Is the plane field integrable? Why?

Raw LaTeX

For any \(p\in\R^3\), let \(K_p\) be the kernel of the form \(2dz-3y\,dx\) taken
at the point \(p\). Then \(K_p\) defines a plane field on the manifold \(\R^3\). Is the
plane field integrable? Why?

Topic Tags

Distributions, Plane Fields, and Frobenius Integrability Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds