On caustics of submanifolds and canal hypersurfaces in Euclidean space

被引：9
|
作者：
Izumiya, Shyuichi [1 ]
Takahashi, Masatomo [2 ]
机构：
[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan
[2] Muroran Inst Technol, Muroran, Hokkaido 0508585, Japan
来源：
TOPOLOGY AND ITS APPLICATIONS | 2012年 / 159卷 / 02期
关键词：
Caustics; Canal hypersurface; Lagrangian singularity; Legendrian singularity; HYPERBOLIC SPACE; WAVE-FRONTS; SINGULARITIES; EVOLUTES; STABILITY;
D O I：
10.1016/j.topol.2011.09.025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate a relationship between the caustics of a submanifold of general dimension and of a canal hypersurface of the submanifold in Euclidean space. As a consequence, these caustics are the same. Moreover, induced Lagrangian immersion germs are Lagrangian equivalent under a suitable condition. In order to show the results, we use the theory of Lagrangian singularity and of Legendrian singularity. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码：501 / 508
页数：8
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