Geodesic
The potential of the Weil-Petersson metric on Torelli space
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 110-120

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It is proved that the function $12\pi\log(Z^\prime(1)/\det\operatorname{Im}\tau)$, where $Z(s)$ is Sel'berg zeta function and $\tau$ is the matrix of the periods of a distinguished Riemann surface, is a potential of the Weil-Petersson metric on the Torelli space. 
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     author = {P. G. Zograf and L. A. Takhtadzhyan},
     title = {The potential of the {Weil-Petersson} metric on {Torelli} space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     volume = {160},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a10/}
}
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P. G. Zograf; L. A. Takhtadzhyan. The potential of the Weil-Petersson metric on Torelli space. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 110-120. http://geodesic.mathdoc.fr/item/ZNSL_1987_160_a10/