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**How to calculate Riemannian Metric by distance function??**

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!!