The complex hyperbolic form as a Weil-Petersson form
Differential Geometry
2024-05-01 v2 Geometric Topology
Abstract
For the moduli space of the punctured spheres, we find a new equality between two symplectic forms defined on it. Namely, by treating the elements of this moduli space as the singular Euclidean metrics on a sphere, we give an interpretation of the complex hyperbolic form, i.e. the K\"ahler form of the complex hyperbolic structure on the moduli space, as a kind of Weil-Petersson form.
Cite
@article{arxiv.2209.10842,
title = {The complex hyperbolic form as a Weil-Petersson form},
author = {Xiangsheng Wang},
journal= {arXiv preprint arXiv:2209.10842},
year = {2024}
}
Comments
v2, 29 pages. Final, various minor improvements according to referee's comment, to appear in Commun. Contemp. Math., the numbering of sections may be different from the published paper