(3) If f is conformal, then f is an isometry.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need help with part (3). Please explain each step and neatly type up. Thank you :)
Transcribed Image Text:Question 4. Let f be a local diffeomorphism between smooth surfaces. Prove the
following statements, or disprove them with a counterexample.
(1) If f is an isometry, then f is equiareal.
(2) If f is equiareal, then f is conformal.
(3) If f is conformal, then f is an isometry.
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