Skip to main content
MathOverflow

Return to Question

deleted 2 characters in body; edited tags
Source Link
François G. Dorais
François G. Dorais
  • 44.4k
  • 6
  • 150
  • 233

On a 2 dimensional surface X is a smooth vector field with isolated zeros. When is there a vector field Y such that the Lie bracket [x,Y] is equal to fY for some given function f on the surface minus the zeros?

Is this problem always solvable locally? If so, what determines whether a local solution can be extended to the entire vector field?

On a 2 dimensional surface X is a smooth vector field with isolated zeros. When is there a vector field Y such that the Lie bracket [x,Y] is equal to fY for some given function f on the surface minus the zeros?

Is this problem always solvable locally? If so, what determines whether a local solution can be extended to the entire vector field?

On a 2 dimensional surface X is a smooth vector field with isolated zeros. When is there a vector field Y such that the Lie bracket [x,Y] is equal to fY for some given function f on the surface minus the zeros?

Is this problem always solvable locally? If so, what determines whether a local solution can be extended to the entire vector field?

Source Link
marc
marc
  • 439
  • 2
  • 6

Solving a simple PDE on a 2 dimensional manifold

On a 2 dimensional surface X is a smooth vector field with isolated zeros. When is there a vector field Y such that the Lie bracket [x,Y] is equal to fY for some given function f on the surface minus the zeros?

Is this problem always solvable locally? If so, what determines whether a local solution can be extended to the entire vector field?