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From the stereographic projection of the Lobachevsky plane from the north pole (0, 0, -R) on disk D a) Calculate the metric dl² induced on disk D by the projection and show that it is conformal. The pair (D², dl² ) will be called the Poincaré disk and is a model for the hyperbolic geometry b) Calculate the length of a diameter of (D², dl²) in that metric.

From the stereographic projection of the Lobachevsky plane from the north pole (0, 0, -R) on disk D a) Calculate the metric dl² induced on disk D by the projection and show that it is conformal. The pair (D², dl² ) will be called the Poincaré disk and is a model for the hyperbolic geometry b) Calculate the length of a diameter of (D², dl²) in that metric.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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From the stereographic projection of the Lobachevsky plane from the north pole (0, 0, -R) on disk D a) Calculate the metric dl² induced on disk D by the projection and show that it is conformal. The pair (D², dl² ) will be called the Poincaré disk and is a model for the hyperbolic geometry b) Calculate the length of a diameter of (D²/2,d1²) in that metric.
Transcribed Image Text:From the stereographic projection of the Lobachevsky plane from the north pole (0, 0, -R) on disk D a) Calculate the metric dl² induced on disk D by the projection and show that it is conformal. The pair (D², dl² ) will be called the Poincaré disk and is a model for the hyperbolic geometry b) Calculate the length of a diameter of (D²/2,d1²) in that metric.
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