where a, b, c, d are real numbers, and ''ad'' − ''bc'' ≠ 0. It is an automorphism of the [[Riemann Sphere]], and the set of all Möbius transformations on the Riemann sphere forms the automorphism group. | where a, b, c, d are real numbers, and ''ad'' − ''bc'' ≠ 0. It is an automorphism of the [[Riemann Sphere]], and the set of all Möbius transformations on the Riemann sphere forms the automorphism group. |