On differential invariants of parabolic surfaces

IF 1.5 3区数学 Q1 MATHEMATICS

Dissertationes Mathematicae Pub Date : 2019-08-21 DOI:10.4064/DM816-8-2020

Zhangchi Chen, J. Merker

引用次数: 14

Abstract

The algebra of differential invariants under $SA_3(\mathbb{R})$ of generic parabolic surfaces $S^2 \subset \mathbb{R}^3$ with nonvanishing Pocchiola $4^{\text{th}}$ invariant $W$ is shown to be generated, through invariant differentiations, by only one other invariant, $M$, of order $5$, having $57$ differential monomials. The proof is based on Fels-Olver's recurrence formulas, pulled back to the parabolic jet bundles.

查看原文本刊更多论文

关于抛物曲面的微分不变量

一般抛物曲面$S^2 \子集$ mathbb{R}^3$具有非消失的Pocchiola $4^{\text{th}}$不变量$W$下的$SA_3(\mathbb{R})$下的微分不变量代数，证明了仅由$5$阶的$M$一个具有$57$微分单项式的$M$通过不变微分生成。这个证明是基于Fels-Olver的递归公式，回到抛物线射流束。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Dissertationes Mathematicae 数学-数学

CiteScore

2.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： DISSERTATIONES MATHEMATICAE publishes long research papers (preferably 50-100 pages) in any area of mathematics. An important feature of papers accepted for publication should be their utility for a broad readership of specialists in the domain. In particular, the papers should be to some reasonable extent self-contained. The paper version is considered as primary. The following criteria are taken into account in the reviewing procedure: correctness, mathematical level, mathematical novelty, utility for a broad readership of specialists in the domain, language and editorial aspects. The Editors have adopted appropriate procedures to avoid ghostwriting and guest authorship.