Editing Möbius transformation (section)

=== Hyperbolic space ===
As seen above, the Möbius group {{nowrap|PSL(2, '''C''')}} acts on Minkowski space as the group of those isometries that preserve the origin, the orientation of space and the direction of time. Restricting to the points where {{nowrap|1=''Q'' = 1}} in the positive light cone, which form a model of [[hyperbolic space|hyperbolic 3-space]] ''H''{{i sup|3}}, we see that the Möbius group acts on ''H''{{i sup|3}} as a group of orientation-preserving isometries. In fact, the Möbius group is equal to the group of orientation-preserving isometries of hyperbolic 3-space. If we use the [[Poincaré disk model|Poincaré ball model]], identifying the unit ball in '''R'''<sup>3</sup> with ''H''{{i sup|3}}, then we can think of the Riemann sphere as the "conformal boundary" of ''H''{{i sup|3}}. Every orientation-preserving isometry of ''H''{{i sup|3}} gives rise to a Möbius transformation on the Riemann sphere and vice versa.