
#1
Dec3009, 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. 



#2
Dec3009, 09:43 AM

P: 679

Wouldn't that be equivalent to a 2n coordinates? But I'm not quite sure




#3
Dec3009, 09:49 PM

P: 403

They are called "Complex manifolds"; imporatnt examples in Physics are the CalabiYau manifolds and Riemann surfaces, see:
http://en.wikipedia.org/wiki/Complex_manifold 


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