lestion 4. Let J be a local diffeomorphism bet following statements, or disprove them with a coun (1) If f is an isometry, then f is equiareal.
lestion 4. Let J be a local diffeomorphism bet following statements, or disprove them with a coun (1) If f is an isometry, then f is equiareal.
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: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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