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How to show that the geodesic circles have constant geodesic curvature on a surface of constant curvature?

Thanks

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    Well, the obvious thing to do is to take geodesic polar coordinates. Have you tried that? You should be able to prove that constant Gaussian curvature forces the metric to take a particular form, and this will in turn imply that geodesic circles have constant geodesic curvature.2011-05-11
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    @Zhen Lin: Why is it not possible to simply/algebraically express geodesic curvature in terms of Gaussian curvature and $u_0 $? koletennbert's question has not yet been answered. http://math.stackexchange.com/questions/162474/curvature-of-geodesic-circles-on-surface-with-constant-curvature?rq=12014-09-25
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    I expected to arrive at a result maybe somewhat like $ u_0 K +1/u_0.$2014-09-25

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