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Topic: How to correct for non-standard curvature?
Replies: 3   Last Post: Oct 11, 2010 12:21 PM

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Posts: 2
Registered: 8/28/10
How to correct for non-standard curvature?
Posted: Aug 28, 2010 2:53 PM
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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 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?


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