AI 中文总结
研究关于\(\mathrm{SL}(3,\mathbb{R})\)-希钦分量上伪凯勒结构的比较，通过比较Rungi - Tamburelli的闭2 - 形式与Goldman的辛形式，确定相关半伪凯勒结构性质及与他人结果的一致性。
AI 中文摘要
我们比较了Rungi - Tamburelli构造的闭2 - 形式\(\omega_f\)与Goldman在\(\mathrm{SL}(3,\mathbb{R})\)-希钦分量上的辛形式\(\omega_G\)。特别地，我们确定由Rungi - Tamburelli定义的\(\mathrm{SL}(3,\mathbb{R})\)-希钦分量上的半伪凯勒结构处处非退化，并且在对齐\(\mathfrak{sl}(3,\mathbb{R})\)上的嘉当形式归一化后，与Collier - Toulisse - Wentworth最近发现的结构一致。
英文摘要
We compare the closed $2$-form $ω_f$ constructed by Rungi-Tamburelli and Goldman's symplectic form $ω_G$ on the $\mathrm{SL}(3,\mathbb R)$-Hitchin component. In particular, we establish that the semi-pseudo-Kähler structure on the $\mathrm{SL}(3,\mathbb{R})$-Hitchin component defined by Rungi-Tamburelli is non-degenerate everywhere and, after aligning the normalization of the Killing form on $\mathfrak{sl}(3,\mathbb{R})$, coincides with the one recently found by Collier-Toulisse-Wentworth.
