本文用一个相当初等的方法，说明了如何把一个3维流形嵌入到5维空间中去。
Using an elementary method, we illustrate how a-3-manifold can be embedded into a 5-space in this note.
当失业工人和空闲职位的匹配是有效时，表示经济系统的四维动力系统存在一个稳定的二维流形。
When the match between the unemployed and the vacant positions is efficient, the economic system described by a four-dimensional differential equation system has a stable two-dimensional manifold.
本文讨论黎曼流形里一般余维的常数平均曲率的子流形为全脐子流形的充要条件。
In this paper, we get a necessary and sufficient condition for a generalcodimensional submanifold with constant mean curvature in a Riemannian mani-fold to be a totally umbilical submanifold.
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