Geodesic
Harmonic Metrics for Higgs Bundles of Rank 3in the Hitchin Section
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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Given a tuple of holomorphic differentials on a Riemann surface, one can define a Higgs bundle in the Hitchin section and a natural symmetric pairing of the Higgs bundle. We study whether a Higgs bundle of rank 3 in the Hitchin section has a compatible harmonic metric when the spectral curve is a 2-sheeted branched covering of the Riemann surface. In particular, we give a condition for Higgs bundles in the Hitchin section on $\mathbb{C}$ or $\mathbb{C}^*$ to have compatible harmonic metrics.
Keywords: Higgs bundles, Hitchin section, harmonic metrics. 
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     author = {Hitoshi Fujioka},
     title = {Harmonic {Metrics} for {Higgs} {Bundles} of {Rank} 3in the {Hitchin} {Section}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a110/}
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Hitoshi Fujioka. Harmonic Metrics for Higgs Bundles of Rank 3in the Hitchin Section. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a110/

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