This article shows that for generic choice of Riemannian metric on a compact oriented manifold M of dimension four, the tangent planes at any self-intersection \(p \in M\) of any prime closed parametrized minimal surface in M are not simultaneously complex for any orthogonal complex structure on M at p. This implies via geometric measure theory that \(H_2(M;{{\mathbb {Z}}})\) is generated by homology classes that are represented by oriented imbedded minimal surfaces.

中文翻译：

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通用黎曼流形中封闭参数化最小曲面的自相交

本文示出了对于黎曼度量的上一个紧凑的定向流形通用的选择中号尺寸的四个，在任何自相交切面\（P \以M \）任何素的封闭在参数化最小的表面中号不是用于同时复杂M在p处的任何正交复结构。通过几何测度理论，这意味着\（H_2（M; {{\ mathbb {Z}}}）\）由同源类生成，这些同源类由定向嵌入的最小曲面表示。