Hey sepoto.

What are the limits for sigma (since it is on a spherical geometry, it must be bounded)?

Remember that because you have a spherical geometry (with different curvature to that of a flat or hyperbolic geometry), that the limits will be bounded and that the sine of this distance will correspond to the circular arc on your sphere that corresponds with the distance away from a point.

A good way to visualize this is to think of a graph of a sine wave in two dimensions that only depend on the distance away from the origin. You will basically get a graph that shows ripples spreading out-ward from the origin (like when you cast a stone in a pond).

It would help immensely if you told us what your limits were and if they were "normalized" (say in the region of 0 to pi or something similar) and what this equation is being used for.