GENERIC LINEAR PERTURBATIONS

被引：3
|
作者：
Ichiki, Shunsuke [1 ]
机构：
[1] Yokohama Natl Univ, Grad Sch Environm & Informat Sci, Yokohama, Kanagawa 2408501, Japan
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 11期
关键词：
Generic linear perturbation; generic projection; stability; modular submanifold; transversality; DISTANCE-SQUARED MAPPINGS; QUADRATIC POLYNOMIAL-MAPPINGS; PLANE; SINGULARITIES; PROJECTIONS;
D O I：
10.1090/proc/14094
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In his celebrated paper Generic projections, John Mather has shown that almost all linear projections from a submanifold of a vector space into a subspace are transverse with respect to a given modular submanifold. In this paper, an improvement of Mather's result is stated. Namely, we show that almost all linear perturbations of a smooth mapping from a submanifold of R-m into R-l yield a transverse mapping with respect to a given modular submanifold. Moreover, applications of this result are given.
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页码：4981 / 4991
页数：11
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