# Constant curvature geodesic circles on a surface with constant Gauss curvature

Is it possible to combine further the last two of the three equations in the link given above into a single ODE / PDE to obtain constant geodesic curvature = 1/b?

Aim is to get an equation for u = constant "circles" or loops on surface of constant Gauss curvature K = 1/a^2, ( b not equal to a ) in geodesic polar coordinates in general.

Or, is the last equation alone adequate to define the boundary for all constant K surfaces?

I attempted to numerically find a solution in a procedure that computes constant geodesic curvature in case of constant K surfaces of revolution, positive and negative K, am attaching what might serve as a representative image:

http://i58.tinypic.com/2mm7o06.jpg