Complex curvilinear coordinates(?)

In summary, a system of curvilinear coordinates can be represented by a set of real scalar functions. It is possible to form a system of curvilinear coordinates with complex valued functions, which would result in 2n coordinates. These are known as "Complex manifolds" and have important applications in Physics, such as the Calabi-Yau manifolds and Riemann surfaces. However, there is limited information available on this topic online.
  • #1
mnb96
715
5
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.
 
Physics news on Phys.org
  • #2
Wouldn't that be equivalent to a 2n coordinates? But I'm not quite sure
 
  • #3

What are complex curvilinear coordinates?

Complex curvilinear coordinates are a type of coordinate system used in mathematics and physics to describe the position of a point in a space with curved dimensions. Unlike Cartesian coordinates, which use straight lines, complex curvilinear coordinates use curved lines to define the position of a point.

What are the advantages of using complex curvilinear coordinates?

Complex curvilinear coordinates have several advantages over other coordinate systems. They are particularly useful for describing objects with curved shapes, such as spheres or ellipsoids. They also make it easier to solve certain types of equations, and can simplify calculations in areas such as fluid dynamics and electromagnetism.

How are complex curvilinear coordinates different from regular curvilinear coordinates?

Regular curvilinear coordinates are based on real numbers, while complex curvilinear coordinates use complex numbers. This means that complex curvilinear coordinates allow for more flexibility and precision in describing curved spaces, and can often provide more accurate results in mathematical models and calculations.

What are some common examples of complex curvilinear coordinates?

Some common examples of complex curvilinear coordinates include polar coordinates, cylindrical coordinates, and spherical coordinates. These coordinate systems are often used in physics and engineering to describe the position and motion of objects in space.

How are complex curvilinear coordinates used in real-world applications?

Complex curvilinear coordinates have a wide range of applications in various fields, including physics, engineering, and computer graphics. They are used to describe the motion of celestial bodies, study the flow of fluids, and model the behavior of electromagnetic fields. They are also used in computer graphics to create 3D models and animations.

Similar threads

I Component definition in curvilinear coordinates
    • Differential Geometry
Replies
1
Views
2K
Curvilinear coordinates on tangent spaces
    • Differential Geometry
Replies
1
Views
2K
Curvilinear coordinate systems and periodic coordinates
    • Differential Geometry
Replies
4
Views
3K
Divergence Theorem in Curvilinear Coordinates: Questions & Explanations
    • Calculus and Beyond Homework Help
Replies
1
Views
860
Lie groups actions and curvilinear coordinates question
    • Differential Geometry
Replies
1
Views
2K
Curvilinear coordinates question
    • Differential Geometry
Replies
4
Views
3K
I What's the underlying frame of the Einstein's Field Equation?
    • Special and General Relativity
6
Replies
186
Views
7K
Curvilinear coordinates from orbits
    • Differential Geometry
Replies
4
Views
3K
I Connection b/w curvature and gravitational field-removing coordinate transformations
    • Special and General Relativity
2
Replies
40
Views
2K
I Demo of cosine direction with curvilinear coordinates
    • General Math
Replies
16
Views
2K

Hot Threads

Recent Insights

Back
Top