4. (a) Show that there exists no surface parametrized by X(u, v) such that E = G = 2023, F = 0, and e = 1, g = -1, f = 2023 in an open set. (b) Suppose X: US is an isothermal parametrization, that is, E = G = x(u, v) > 0 and F = 0. Show that the Gauss curvature 1 21 (log A), here A is the Laplacian operator defined by Af = fuu + fvv. K=--
4. (a) Show that there exists no surface parametrized by X(u, v) such that E = G = 2023, F = 0, and e = 1, g = -1, f = 2023 in an open set. (b) Suppose X: US is an isothermal parametrization, that is, E = G = x(u, v) > 0 and F = 0. Show that the Gauss curvature 1 21 (log A), here A is the Laplacian operator defined by Af = fuu + fvv. K=--
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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