从R^n到R^3的光滑映射的generic奇点

THE GENERIC SINGULARITIES OF SMOOTH MAPS FROM R n TO R 3

本文的目的在于用微分拓扑的方法讨论从Ｒｎ 到Ｒ３的光滑映射的ｇｅｎｅｒｉｃ 奇点的分类问题，我们证明这样的映射只有三类奇点：折点、尖点和燕尾点，并给出了它们的标准型．这推广了Ｊ． Ｍａｒｔｉｎｅｔ［１］ 的结果．

The aim of this paper is to study the classification problem of generic singularities of smooth maps from R n to R 3. We prove that there are three kinds of singularities of such maps: folds, cusps and swallowtail points, and we give their standard forms. It developes the results of J. Martinet [1].