We study a natural functional on the space of holomorphic sections of the Deligne-Hitchin moduli space of a compact Riemann surface, generalizing the energy of equivariant harmonic maps corresponding to twistor lines. We give a link to a natural meromorphic connection on the hyperholomorphic line bundle recently constructed by Hitchin. Moreover, we prove that for a certain class of real holomorphic sections of the Deligne-Hitchin moduli space, the functional is basically given by the Willmore energy of corresponding (equivariant) conformal map to the 3-sphere. As an application we use the functional to distinguish new components of real holomorphic sections of the Deligne-Hitchin moduli space from the space of twistor lines.

中文翻译：

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Deligne-Hitchin 扭曲空间部分的能量

我们研究了紧致黎曼曲面的 Deligne-Hitchin 模空间的全纯截面空间上的自然泛函，概括了对应于扭曲线的等变调和映射的能量。我们在 Hitchin 最近构建的超全纯线丛上给出了一个自然亚纯连接的链接。此外，我们证明了对于 Deligne-Hitchin 模空间的某一类实全纯截面，泛函基本上由对应（等变）共形映射到 3 球体的 Willmore 能量给出。作为一个应用程序，我们使用泛函来区分 Deligne-Hitchin 模空间的真实全纯截面的新分量与扭曲线空间。