10. Let (s, t) be a coordinate patch for a smooth surface S with F = 0. Prove that if all s- curves and t- curves are geodesics, then S is flat.
10. Let (s, t) be a coordinate patch for a smooth surface S with F = 0. Prove that if all s- curves and t- curves are geodesics, then S is flat.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 39RE
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![10. Let (s, t) be a coordinate patch for a smooth surface S with F = 0. Prove that if all s- curves and t-
curves are geodesics, then S is flat.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffac2294e-50fc-4aa5-b57c-52fe5ca318ae%2Fb06b2e6e-ddb7-4897-96e9-83bdaa801125%2Fxy2ma3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10. Let (s, t) be a coordinate patch for a smooth surface S with F = 0. Prove that if all s- curves and t-
curves are geodesics, then S is flat.
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