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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2014 • Question 4

Question

Math 6510 • Differentiable Manifolds Spring 2014 • Question 4

Let \(W\) be a vector field on a smooth manifold \(M\) and assume that \(V\) has a flow that is defined on all of \(M\) and for all time. Let \(V\) be another vector field on \(M\) such that \(V-W\) has compact support. Show that \(V\) has a flow on all of \(M\) defined for all time.

Raw LaTeX

Let \(W\) be a vector field on a smooth manifold \(M\) and assume that \(V\) has
a flow that is defined on all of \(M\) and for all time. Let \(V\) be another vector
field on \(M\) such that \(V-W\) has compact support. Show that \(V\) has a flow on all
of \(M\) defined for all time.

Topic Tags

Compactly Supported Forms and Integration Left-Invariant Vector Fields Smooth Manifolds and Embedded Submanifolds Vector Fields and Flows