The Weil-Petersson metric geometry
Differential Geometry
2008-01-03 v1
Abstract
A summary introduction of the Weil-Petersson metric space geometry is presented. Teichmueller space and its augmentation are described in terms of Fenchel-Nielsen coordinates. Formulas for the gradients and Hessians of geodesic-length functions are presented. Applications are considered. A description of the Weil-Petersson metric in Fenchel-Nielsen coordinates is presented. The Alexandrov tangent cone at points of the augmentation is described. A comparison dictionary is presented between the geometry of the space of flat tori and Teichmueller space with the Weil-Petersson metric.
Keywords
Cite
@article{arxiv.0801.0175,
title = {The Weil-Petersson metric geometry},
author = {Scott A. Wolpert},
journal= {arXiv preprint arXiv:0801.0175},
year = {2008}
}