{"title":"关于抛物曲面的微分不变量","authors":"Zhangchi Chen, J. Merker","doi":"10.4064/DM816-8-2020","DOIUrl":null,"url":null,"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.","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":" ","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2019-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"On differential invariants of parabolic surfaces\",\"authors\":\"Zhangchi Chen, J. Merker\",\"doi\":\"10.4064/DM816-8-2020\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":51016,\"journal\":{\"name\":\"Dissertationes Mathematicae\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2019-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dissertationes Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/DM816-8-2020\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dissertationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/DM816-8-2020","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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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.
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