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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2005 • Question 5

Question

Math 6510 • Differentiable Manifolds Winter 2005 • Question 5

Let \[ X=y\frac {\partial }{\partial x}-(x+1)\frac {\partial }{\partial y} \] and \[ Y=y\frac {\partial }{\partial x}-(x-1)\frac {\partial }{\partial y} \] be two vector fields in \(\mathbb {R}^2\). Compute \([X,Y]\).

Raw LaTeX

Let
\[
  X=y\frac{\partial}{\partial x}-(x+1)\frac{\partial}{\partial y}
\]
and
\[
  Y=y\frac{\partial}{\partial x}-(x-1)\frac{\partial}{\partial y}
\]
be two vector fields in \(\mathbb{R}^2\). Compute \([X,Y]\).

Topic Tags

Left-Invariant Vector Fields Vector Fields and Flows