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1. A diffeomorphism f : E' between surfaces is a conformal map, if there is a non- vanishing function A so that p(X) = (.1) for all P € and X E TpL The function l is called the conformal factor. a. Let Q : u V be an orientation preserving diffeomorphism of open subsets of R² and write (u,v) = (D1(u,0), , I2 (u,v)) . Show that Q is conformal if and only if 201 202 and 001 002 ou du du ou b. Give an expression for the conformal factor.

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Differential Geometry Question
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