论文标题
排名一号子手机的分类
Classification of rank-one submanifolds
论文作者
论文摘要
我们研究了欧几里得空间的统治统治。首先，对于每个（参数化的）统治submanifold $σ$，我们将一个称为学位的整数值函数关联，以衡量$σ$无法圆柱形的程度。特别是，我们表明，如果该学位是恒定的，则等于$ d $，那么$σ$的奇异性只能沿$（m-d）$ - 维度“效果” submanifold发生。该结果使我们能够将$ \ Mathbb {r}^{3} $中可开发表面的标准分类扩展到整个平面和统治的无平面点，也称为rank-One：cand-One Submanifold的一个开放和密集的子集，每个等级的子集的每个等级，都是cylindrical，cylindrical，锥形的，锥形的，锥形和切线的结合。
We study ruled submanifolds of Euclidean space. First, to each (parametrized) ruled submanifold $σ$, we associate an integer-valued function, called degree, measuring the extent to which $σ$ fails to be cylindrical. In particular, we show that if the degree is constant and equal to $d$, then the singularities of $σ$ can only occur along an $(m-d)$-dimensional "striction" submanifold. This result allows us to extend the standard classification of developable surfaces in $\mathbb{R}^{3}$ to the whole family of flat and ruled submanifolds without planar points, also known as rank-one: an open and dense subset of every rank-one submanifold is the union of cylindrical, conical, and tangent regions.
