Let S be a surface with genus g and n punctures and let x(S)=3g+n denote the complexity of the surface S. We prove that in the Teichmüller space T(S) endowed with the Weil-Petersson metric, every Teichmüller geodesics segment fellow-travels the Weil-Petersson geodesic segment with the same pair of end points if and only if x(S)=5.
Gokturk, Ali,
"Comparison of Teichmüller geodesics and Weil-Petersson geodesics"
(2011).
Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0SN076B
