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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2010 • Question 2

Question

Math 6510 • Differentiable Manifolds Fall 2010 • Question 2

Suppose \(M\) is a smooth manifold with a smooth plane field. If the plane field is integrable, then prove that the bracket of any pair of smooth vector fields on \(M\) that are tangent to the plane field is another smooth vector field on \(M\) that is tangent to the plane field.

Raw LaTeX

Suppose \(M\) is a smooth manifold with a smooth plane field. If the plane field
is integrable, then prove that the bracket of any pair of smooth vector fields on
\(M\) that are tangent to the plane field is another smooth vector field on \(M\) that
is tangent to the plane field.

Topic Tags

Distributions, Plane Fields, and Frobenius Integrability Left-Invariant Vector Fields Smooth Manifolds and Embedded Submanifolds Vector Fields and Flows