Global comparison of pseudo-Kähler structures on the SL(3,ℝ)-Hitchin component

2026/07/22 by Andrea Tamburelli
#math.DG

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Abstract

We compare the closed 2-form ω_f constructed by Rungi-Tamburelli and Goldman's symplectic form ω_G on the SL(3,\mathbb R)-Hitchin component. In particular, we establish that the semi-pseudo-Kähler structure on the SL(3,ℝ)-Hitchin component defined by Rungi-Tamburelli is non-degenerate everywhere and, after aligning the normalization of the Killing form on \mathfraksl(3,ℝ), coincides with the one recently found by Collier-Toulisse-Wentworth.

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