Which linear fractional transformations
induce rotations of the sphere?
Abstract: These
notes supplement the discussion of linear fractional mappings
presented in a beginning graduate course in complex analysis.
The goal is to prove that a mapping 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 whose
(twobytwo) coefficient matrix is unitary.
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