Chern-kuiper’s inequalities

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-08-04 DOI:10.1007/s10231-024-01492-6

Diego Guajardo

引用次数: 0

Abstract

Given a Euclidean submanifold $g:M^{n}\rightarrow {\mathbb {R}}^{n+p}$, Chern and Kuiper provided inequalities between $\mu $ and $\nu _g$, the ranks of the nullity of $M^n$ and the relative nullity of g respectively. Namely, they prove that

$$\begin{aligned} \nu _g\le \mu \le \nu _g+p. \end{aligned}$$(1)

In this work, we study the submanifolds with $\nu _g\ne \mu $. More precisely, we characterize locally the ones with $0\ne (\mu -\nu _g)\in \{p,p-1,p-2\}$ under the hypothesis of $\nu _g\le n-p-1$.

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Chern-kuiper 不等式

给定一个欧几里得子平面（g:M^{n}\rightarrow {mathbb {R}}^{n+p}\ ），Chern 和 Kuiper 提供了 $\mu $ 和 $\nu _g$之间的不等式，它们分别是 $M^n$ 的无效性等级和 g 的相对无效性等级。也就是说，他们证明了 $$\begin{aligned}\g+p.\end{aligned}$$(1)This work, we study the submanifolds with $\nu _g\ne \mu $。更准确地说，我们在$\nu _g\le n-p-1$的假设下局部地描述了那些具有$0\ne (\mu -\nu _g)\in\{p,p-1,p-2\}$的子曲面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

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