论文标题
通用riemannian歧管中封闭的参数化最小表面的自身交流
Self-intersections of Closed Parametrized Minimal Surfaces in Generic Riemannian Manifolds
论文作者
论文摘要
本文表明，要在$ m $中的平滑流形$ m $上的riemannian指标上进行通用的选择，$ m $中的所有主要紧凑的参数化最小表面具有以下意义上的自我干扰：自我干扰是横向的，并且在任何自我隔离点上都无法进行任何或$ $ $ $ $ $ $ $ $ $ $ $ $。这意味着Sheldon Chang的结果是$ H_2（M; {\ Mathbb Z}）$由同源类别以嵌入式最小表面表示的同源类生成。
This article shows that for generic choice of Riemannian metric on a smooth manifold $M$ of dimension four, all prime compact parametrized minimal surfaces within $M$ have self-intersections in general position in the following sense: self-intersections are transverse and the two tangent planes at any self-intersection point fail to be complex with respect to any orthogonal complex structure on the ambient manifold $M$. This implies via a result of Sheldon Chang that $H_2(M;{\mathbb Z})$ is generated by homology classes that are represented by imbedded minimal surfaces.
