Let H={(u,v)∈R2:v>0} be the upper half-plane model of the hyper... | Filo
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Consider the upper half plane model U = {(x,y) ∈ R^2 : y > 0}... | Filo
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SOLVED:If a is a point of the upper half-plane, show that the Möbius transformation g given by g(z)=(z-a)/(z-a̅) defines an isometry from the upper half-plane model H to the disc model D of the hyperbolic plane, sending a to zero. Deduce that for points z1, z2 in the upper halfplane, the hyperbolic distance is given by ρ(z1, z2)=2 tanh^-1|(z1-32)/(l)|,
SOLVED:If a is a point of the upper half-plane, show that the Möbius tr…
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