Complex curvilinear coordinates(?)

1. Dec 30, 2009

mnb96

Hello,
a system of curvilinear coordinates is usually expressed by an admissible transformation represented by a set of real scalar functions $x_i=x_i(u_1,\ldots,u_n)$.

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. Dec 30, 2009

kof9595995

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

3. Dec 30, 2009