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Weil-Petersson metric on deformation spaces

Huai-Dong Cao Department of Mathematics, Lehigh University, Bethlehem, PA 18015, USA Xiaofeng Sun Department of Mathematics, Lehigh University, Bethlehem, PA 18015, USA Shing-Tung Yau Department of Mathematics, Harvard University, Cambridge, MA 02138, USA Yingying Zhang Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China

Differential Geometry mathscidoc:2204.10009

Journal of the Iranian Mathematical Society, 1, (1), 1-12, 2020.6
In this paper we survey certain aspects of the classical Weil-Petersson metric and its generalizations. Being a natural L^2 metric on the parameter space of a family of complex manifolds or holomorphic vector bundles which admit some canonical metrics, the Weil-Petersson metric is well defined when the automorphism group of each fiber is discrete and the curvature of the Weil-Petersson metric can be computed via certain integrals over each fiber. We will discuss the case when these fibers have continuous automorphism groups. We also discuss the relation between the Weil-Petersson metric and energy of harmonic maps.
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@inproceedings{huai-dong2020weil-petersson,
  title={Weil-Petersson metric on deformation spaces},
  author={Huai-Dong Cao, Xiaofeng Sun, Shing-Tung Yau, and Yingying Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428140754782667145},
  booktitle={Journal of the Iranian Mathematical Society},
  volume={1},
  number={1},
  pages={1-12},
  year={2020},
}
Huai-Dong Cao, Xiaofeng Sun, Shing-Tung Yau, and Yingying Zhang. Weil-Petersson metric on deformation spaces. 2020. Vol. 1. In Journal of the Iranian Mathematical Society. pp.1-12. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428140754782667145.
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