Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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N. Rungi - A. Tamburelli

The $\mathbb{P}\mathrm{S}\mathrm{L}(3,\mathbb{R})$-Hitchin component as an infinite-dimensional pseudo-Kähler reduction

created by rungi on 02 Dec 2023



Inserted: 2 dec 2023
Last Updated: 2 dec 2023

Year: 2023

ArXiv: 2306.02699 PDF


The aim of this paper is to show the existence and give an explicit description of a pseudo-Riemannian metric and a symplectic form on the $\mathbb{P}\mathrm{S}\mathrm{L}(3,\mathbb{R})$-Hitchin component, both compatible with Labourie and Loftin's complex structure. In particular, they give rise to a mapping class group invariant pseudo-K\"ahler structure on a neighborhood of the Fuchsian locus, which restricts to a multiple of the Weil-Petersson metric on Teichm\"uller space. Finally, generalizing a previous result in the case of the torus, we prove the existence of an Hamiltonian $S^1$-action.

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