Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1999 • Question 3

Question

Math 6510 • Differentiable Manifolds Fall 1999 • Question 3

Prove that the \(n\)-sphere admits a nowhere vanishing vector field if and only if \(n\) is odd.

Raw LaTeX

Prove that the \(n\)-sphere admits a nowhere vanishing vector field if and only if
\(n\) is odd.

Topic Tags

Left-Invariant Vector Fields Vector Fields and Flows