- #1
mnb96
- 715
- 5
Hello,
I read somewhere that in 2D, the Möbius transformations do not represent all the possible conformal transformations, while according to Liouville's theorem, in spaces of dimension greater than 2 all the conformal transformation can be expressed as combinations of scaling/translation/rotation/inversion (=Möbius transformations).
Can anyone mention what are the conformal transformations of the plane that cannot be "captured" by Möbius transformations?
Thanks.
I read somewhere that in 2D, the Möbius transformations do not represent all the possible conformal transformations, while according to Liouville's theorem, in spaces of dimension greater than 2 all the conformal transformation can be expressed as combinations of scaling/translation/rotation/inversion (=Möbius transformations).
Can anyone mention what are the conformal transformations of the plane that cannot be "captured" by Möbius transformations?
Thanks.