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

页码：501 / 508

页数：8

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