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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2013 • Question 4

Question

Math 6510 • Differentiable Manifolds Fall 2013 • Question 4

Let \(\Delta \) be a plane field on a manifold \(M\) and let \(X,Y\) be two vector fields tangent to \(\Delta \). Show that if for some \(p\in M\) we have \(Y_p=0\) then \([X,Y]_p\in \Delta \).

Raw LaTeX

Let \(\Delta\) be a plane field on a manifold \(M\) and let \(X,Y\) be two vector
fields tangent to \(\Delta\). Show that if for some \(p\in M\) we have \(Y_p=0\) then
\([X,Y]_p\in\Delta\).

Topic Tags

Distributions, Plane Fields, and Frobenius Integrability Left-Invariant Vector Fields Tangent Bundles and Vector Bundles Vector Fields and Flows