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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.

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.

Advanced Engineering Mathematics
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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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.
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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