Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Out of curiosity, is there a nice characterization of the linear fractional transformations which give rotations of the Riemann sphere?

My thinking was a rotation of the Riemann sphere rotates about some axis, and the two points where the sphere intersects the axis will be two fixed points. What more be said of this?

share|cite|improve this question
up vote 4 down vote accepted

Yes, there is! See this for details.

"A map of the Riemann sphere to itself is a rotation if and only if the corresponding map induced on the plane by stereographic projection is a linear fractional transformation whose coefficient matrix is unitary."

share|cite|improve this answer
Thanks for the reference. – Dedede Feb 13 '12 at 8:53

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.