I am given a hyperbolic space of constant negative curvature 'k' and a circle of radius 'R'. How do I get the circumference and the area of the circle? My problem is that I know the answer only for the case when 'k=-1', but my space can have any possible (negative) curvature, possibly different from '-1'. I have the feeling that these formulas must somehow be corrected for non-standard curvature.
And if we are at it: Is there a generic formula for circle circumference and area, which is somehow valid for spherical as well as Euclidean and hyperbolic spaces of different curvature?