1. Consider the patcho (u, v) = (u, v, u² + v²)where u, v ER.(a)Find the formula for the Gauss map G, and describe geometrically its image.(b) Compute the Weingarten map W of o.(c).Use (b) to compute the Gaussian curvature of o.

Part(a): Given function is, σu,v=u,v,u2+v2 u,v∈ℝDiffrentiating partially with respect to…

Consider the patch o (u, v) = (u, v, u² + v²) here u, v E R. Find the formula for the Gauss map G, and describe geometrically its image. 2 Compute the Weingarten map W of o. Use (b) to compute the Gaussian curvature of o.

Consider the patch o (u, v) = (u, v, u² + v²) here u, v E R. Find the formula for the Gauss map G, and describe geometrically its image. 2 Compute the Weingarten map W of o. Use (b) to compute the Gaussian curvature of o.

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 33E

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Question

1. Consider the patch
o (u, v) = (u, v, u² + v²)
where u, v ER.
(a)
Find the formula for the Gauss map G, and describe geometrically its image.
(b) Compute the Weingarten map W of o.
(c).
Use (b) to compute the Gaussian curvature of o.

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