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Complex curvilinear coordinates(?)

by mnb96
Tags: complex, coordinates, curvilinear
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mnb96
#1
Dec30-09, 09:32 AM
P: 625
Hello,
a system of curvilinear coordinates is usually expressed by an admissible transformation represented by a set of real scalar functions [itex]x_i=x_i(u_1,\ldots,u_n)[/itex].

Does it make sense to form a system of curvilinear coordinates where the [itex]x_i[/tex] and [itex]u_i[/tex] functions are complex valued?
If that exists, I cannot find any source in the net.
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kof9595995
#2
Dec30-09, 09:43 AM
P: 679
Wouldn't that be equivalent to a 2n coordinates? But I'm not quite sure
JSuarez
#3
Dec30-09, 09:49 PM
P: 402
They are called "Complex manifolds"; imporatnt examples in Physics are the Calabi-Yau manifolds and Riemann surfaces, see:

http://en.wikipedia.org/wiki/Complex_manifold


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