一般直线同余的奇异性

Pub Date : 2021-08-14 DOI:10.2969/jmsj/88348834

M. Craizer, Ronaldo Garcia

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引用次数: 2

摘要

直线同余是三维空间中的二维直线族。在一般线同余中出现的奇点是褶皱、尖点和燕尾([7])。本文给出了这些奇异点的几何描述。使用的主要工具是定义一般直线同余的等仿射对的存在性。数学学科分类(2010)。53a55, 57r45, 53a20。

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Singularities of generic line congruences

Line congruences are 2-dimensional families of lines in 3space. The singularities that appear in generic line congruences are folds, cusps and swallowtails ([7]). In this paper we give a geometric description of these singularities. The main tool used is the existence of an equiaffine pair defining a generic line congruence. Mathematics Subject Classification (2010). 53A55, 57R45, 53A20.

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