Understanding Weil-Petersson curvature
Differential Geometry
2008-09-23 v1 Geometric Topology
Abstract
A brief history of the investigation of the Weil-Petersson curvature and a summary of Teichm\"{u}ller theory are provided. A report is presented on the program to describe an intrinsic geometry with the Weil-Petersson metric and geodesic-length functions. Formulas for the metric, covariant derivative and formulas for the curvature tensor are presented. A discussion of methods is included. Recent and new applications are sketched, including results from the work of Liu-Sun-Yau, an examination of the Yamada model metric and a description of Jacobi fields along geodesics to the boundary.
Cite
@article{arxiv.0809.3699,
title = {Understanding Weil-Petersson curvature},
author = {Scott A. Wolpert},
journal= {arXiv preprint arXiv:0809.3699},
year = {2008}
}