J-holomorphic curves in nearly Kähler \(\mathbb {CP}^3\) are related to minimal surfaces in \(S^4\) as well as associative submanifolds in \(\Lambda ^2_-(S^4)\). We introduce the class of transverse J-holomorphic curves and establish a Bonnet-type theorem for them. We classify flat tori in \(S^4\) and construct moment-type maps from \(\mathbb {CP}^3\) to relate them to the theory of \(\mathrm {U}(1)\)-invariant minimal surfaces on \(S^4\).

中文翻译：

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近 Kähler $$\mathbb {CP}^3$$ CP 3 中的横向 J 全纯曲线

近 Kähler 中的J -全纯曲线\(\mathbb {CP}^3\)与\(S^4\) 中的最小曲面以及\(\Lambda ^2_-(S^4)\ 中的关联子流形有关)。我们引入了横向J-全纯曲线的类，并为它们建立了Bonnet型定理。我们在\(S^4\) 中对平面环进行分类，并从\(\mathbb {CP}^3\)构建矩型映射，将它们与\(\mathrm {U}(1)\)的理论联系起来- \(S^4\)上的不变最小曲面。