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rg0now
Posts:
2
Registered:
8/28/10


How to correct for nonstandard curvature?
Posted:
Aug 28, 2010 2:53 PM


Dear all,
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 nonstandard 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?
Thanks, Gabor



