For a given minimal surface in the n-sphere, two ways to construct a minimal surface in the m-sphere are given. One way constructs a minimal immersion. The other way constructs a minimal immersion which may have branch points. The branch points occur exactly at each point where the original minimal surface is geodesic. If a minimal surface in the 3-sphere is given, then these ways construct Lawson’s polar variety and bipolar surface.

中文翻译：

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n 球体中极小曲面的极性种类和双极性曲面

对于给定的n球面上的最小曲面，给出了在m球面上构造最小曲面的两种方法。一种方法是构建最小的沉浸感。另一种方式构建可能具有分支点的最小沉浸。分支点恰好出现在原始最小表面为测地线的每个点上。如果给定了 3 球体中的最小曲面，则这些方法构造了劳森的极簇和双极曲面。