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I have question about geometry for expert geometry what is the definition of conformal map and the condition? can you please give to me the formula of conformal map. Also is that right that $E=G$ is one of formula for conformal map ? Where this formula comes from ? I need more explain about this part. Thank you very much.

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What are $E$ and $G$ ? – user18119 Feb 26 '13 at 16:30
up vote 1 down vote accepted

The basic meaning of "conformal" in geometry is that the transformation preserves the measure of infinitesimal angles.

For example, a conformal transformation might take the intersection of two straight lines and send it to a line cutting a circle. The line will be "perpendicular" to the circle in the sense that the tangent line at the point of intersection is perpendicular to the line cutting the circle.

Without context, it's impossible to give you a formula for all conformal maps: you need to be more specific! If we want to think about the Euclidean plane, then there is one easy family of conformal linear maps. They can be represented by matrices of the form

$$ \begin{bmatrix}a&b\\-b&a\end{bmatrix} $$ where $a$ and $b$ are real numbers, and at least one is nonzero. But there are more conformal transformations than just the linear ones...

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thank you so much – leena adam Mar 5 '13 at 21:15

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