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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2021 • Question 3

Question

Math 6510 • Differentiable Manifolds Fall 2021 • Question 3

Let \(M\) be a smooth manifold and \(V\) a vector field on \(M\) such that flow for \(V\) is defined for all time. Let \(W\) be another vector field on \(M\) such that \(V\) and \(W\) agree outside of a compact set in \(M\) . Show that \(W\) is defined for all time.

Raw LaTeX

Let \(M\) be a smooth manifold and \(V\) a vector field on \(M\) such that flow
for \(V\) is defined for all time. Let \(W\) be another vector field on \(M\) such
that \(V\) and \(W\) agree outside of a compact set in \(M\) . Show that \(W\) is
defined for all time.

Topic Tags

Homotopy and Degree on Manifolds Left-Invariant Vector Fields Smooth Manifolds and Embedded Submanifolds Vector Fields and Flows