9. Justify why the surfaces below are not pairwise locally isometric (a) Sphere S1 = {(x, y, 2) e R |x? + y + z? = 1} (b) Cylinder S2 = {(x, y, z) € R | x? + y? = 1} %3D %3D (c) Hyperbolic Paraboloid S3 = (x, y, 2) €R |z = x - y²}
9. Justify why the surfaces below are not pairwise locally isometric (a) Sphere S1 = {(x, y, 2) e R |x? + y + z? = 1} (b) Cylinder S2 = {(x, y, z) € R | x? + y? = 1} %3D %3D (c) Hyperbolic Paraboloid S3 = (x, y, 2) €R |z = x - y²}
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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Transcribed Image Text:9. Justify why the surfaces below are not pairwise locally isometric:
(a) Sphere S1 = {(x, y, 2) € R' |x² + y° + z? = 1}
(b) Cylinder S2 = {(x, y, z) € R* | x* + y° = 1}
(c) Hyperbolic Paraboloid S 3 = {(x, y, 2) e R' |z = -y}
%3D
%3D
%3D
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