M\'etriques hyperk\"ahl\'eriennes pli\'ees

TL;DR

This paper introduces a construction for folded hyperKähler metrics inspired by Hitchin's work and proves the local existence of the Hitchin component for SL(∞,R), advancing the understanding of these geometric structures.

Contribution

It provides a new construction method for folded hyperKähler metrics and establishes the local existence of the Hitchin component for SL(∞,R).

Findings

Constructed folded hyperKähler metrics.

Proved local existence of the Hitchin component for SL(∞,R).

Enhanced understanding of hyperKähler geometry in relation to Higgs bundles.

Abstract

N. Hitchin recently introduced the notion of folded hyperK\"ahler metrics, in relation with SL(\infty,R) Higgs bundles. We provide a construction of such metrics, and prove the local existence of the Hitchin component for SL(\infty,R).