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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2013 • Question 5

Question

Math 6510 • Differentiable Manifolds Spring 2013 • Question 5

Is the plane field on \(\mathbb {R}^3\) that is spanned at the point \((x,y,z)\) by \(2\frac {\partial }{\partial x}+y\frac {\partial }{\partial y}\) and \(\frac {\partial }{\partial y}+y\frac {\partial }{\partial z}\) integrable? Explain.

Raw LaTeX

Is the plane field on \(\R^3\) that is spanned at the point \((x,y,z)\) by
\(2\frac{\partial}{\partial x}+y\frac{\partial}{\partial y}\) and
\(\frac{\partial}{\partial y}+y\frac{\partial}{\partial z}\) integrable? Explain.

Topic Tags

Distributions, Plane Fields, and Frobenius Integrability