Please solve the differential geometry problemNo chatgpt pls will upvote. 1. In order to prove that the stereographic projections (from the poles N, S onto the equatorialplane) form an atlas of the 2-sphere check that the transitions function os 71: R² \ {0} →R2\{0} is given by: 500+1(x, y) = x²±² (x, y); in particular we see that it is a diffeomorphism.1x²+y2

To prove that the stereographic projections form an atlas of the 2-sphere, we need to verify that…

Answered: 1. In order to prove that the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 34E

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1. In order to prove that the stereographic projections (from the poles N, S onto the equatorial plane) form an atlas of the 2-sphere check that the transitions function os 71: R² \ {0} → R2\{0} is given by: 500+1(x, y) = x²±² (x, y); in particular we see that it is a diffeomorphism. 1 x²+y2