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<p>In this paper, we study an equation which we call the basic Hitchin equation. This is an equation defined on Sasakian threefolds and is a three-dimensional analog of the Hitchin equation, which is defined on Riemann surfaces. We construct the moduli space of the basic Hitchin equation and show that such a space admits a hyperKähler metric. This also shows that the moduli space of flat bundles over Sasakian threefolds admits a hyperKähler metric. We also calculate the dimension of the moduli space.</p>

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Moduli Spaces of the Basic Hitchin Equation on Sasakian Threefolds

  • 期刊论文

  • 发表日期：

    2026年5月22日

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  • Takashi Ono

摘要

In this paper, we study an equation which we call the basic Hitchin equation. This is an equation defined on Sasakian threefolds and is a three-dimensional analog of the Hitchin equation, which is defined on Riemann surfaces. We construct the moduli space of the basic Hitchin equation and show that such a space admits a hyperKähler metric. This also shows that the moduli space of flat bundles over Sasakian threefolds admits a hyperKähler metric. We also calculate the dimension of the moduli space.