Re: Visualizing a curved space

Thus spake Alan <info@xxxxxxxxxxxxxxxxxxxxxxxxx>
I have a 2D Riemann metric tensor with coordinates (x,y) in a half-plane
-Infinity < x < Infinity, y > 0. I can calculate the geodesics.
I am looking for suggestions on algorithms for visualizations
of the geometry. (Ideally, something I can implement in Mathematica).

The space is somewhat similar to the Poincare hyperbolic
half-plane, in that the metric has the form

ds^2 = a(y) dx^2 + b(y) dy^2

I am a real novice in differential geometry, so the more elementary
the suggestions, the better.

Thanks!
alan


You could draw a field of orthogonal pairs of unit vectors (or vectors
of fixed length). They will need to be stretched by factors 1/a and 1/b
at different parts of the map. Then you can think of the geometry by
inverting the stretch in your mind's eye.




Regards

--
Charles Francis
substitute charles for NotI to email

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