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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?

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up vote 3 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."

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Thanks for the reference. –  Dedede Feb 13 '12 at 8:53
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