How can we define, what a conformal mapping of a curve is? Can we say that this is a map that preserves the oriented angle between any two points on the curve? Or is there an another (better, more accurate) definition?
Many thanks in advance
2026-03-28 13:05:06.1774703106
Conformal mapping of a curve
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I believe by consulting "The Ambient Metric," by Charles Fefferman and C. Robin Graham (Annals of Mathematical Studies, Number 178, Princeton University Press, 2012), you will discover on page 1 that "Conformal geometry is the study of spaces where one knows how to measure infinitesimal angles but not lengths." It goes on to discuss a conformal structure on manifolds. Whether this is of any use to you, I do not know, however I wish you well in your studies.