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Parallel Axioms 1. Show that the Poincaré upper half space model H+ satisfies the hyperbolic parallel axiom. 2. (Harder) Show that there exists a bijective map between the Poincaré upper half space model H+ and the Poincaré disk model P that preserves the distance in each model, i.e. dh (A, B) = dp($(A), ¢(B))

Parallel Axioms 1. Show that the Poincaré upper half space model H+ satisfies the hyperbolic parallel axiom. 2. (Harder) Show that there exists a bijective map between the Poincaré upper half space model H+ and the Poincaré disk model P that preserves the distance in each model, i.e. dh (A, B) = dp($(A), ¢(B))

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Parallel Axioms 1. Show that the Poincaré upper half space model H+ satisfies the hyperbolic parallel axiom. 2. (Harder) Show that there exists a bijective map between the Poincaré upper half space model H+ and the Poincaré disk model P that preserves the distance in each model, i.e. dh (A, B) = dp(ø(A), ¢(B))
Transcribed Image Text:Parallel Axioms 1. Show that the Poincaré upper half space model H+ satisfies the hyperbolic parallel axiom. 2. (Harder) Show that there exists a bijective map between the Poincaré upper half space model H+ and the Poincaré disk model P that preserves the distance in each model, i.e. dh (A, B) = dp(ø(A), ¢(B))
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