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Dear Folks:

Here is the problem: in |z|<1, we difine a distance between any two points z_{1}and z_{2}by d(z_{1}, z_{2}) = ln((z_{1}- b)(z_{2}- a)/((z_{1}- a)(z_{2}- b))) ,where a is the intersection of line z_{1}z_{2}and the circle which is nearer to z_{1}, and b is the other intersection. How to compute the Remannian Metric ds^{2}.

My classmates calculated it indirectly for he knew the background of the problem?? But is there a direct way??

Many thanks!!

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# How to calculate Riemannian Metric by distance function?

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