阿贝尔常微分方程，微分代数和投影连接

IF 0.9 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2024-12-16 DOI:10.1016/j.bulsci.2024.103567

Oumar Wone

{"title":"阿贝尔常微分方程，微分代数和投影连接","authors":"Oumar Wone","doi":"10.1016/j.bulsci.2024.103567","DOIUrl":null,"url":null,"abstract":"<div><div>We firstly study the Abel ordinary differential equations of the first and second kind from the perspectives of differential algebra. Then using differential geometry we exhibit some relations between the Abel ordinary differential equation of the first kind and projective connections on surfaces which allow us to find a “Darboux first integral” of the Abel differential equation.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103567"},"PeriodicalIF":0.9000,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Abel ordinary differential equation, differential algebra and projective connections\",\"authors\":\"Oumar Wone\",\"doi\":\"10.1016/j.bulsci.2024.103567\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We firstly study the Abel ordinary differential equations of the first and second kind from the perspectives of differential algebra. Then using differential geometry we exhibit some relations between the Abel ordinary differential equation of the first kind and projective connections on surfaces which allow us to find a “Darboux first integral” of the Abel differential equation.</div></div>\",\"PeriodicalId\":55313,\"journal\":{\"name\":\"Bulletin des Sciences Mathematiques\",\"volume\":\"199 \",\"pages\":\"Article 103567\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-12-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin des Sciences Mathematiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0007449724001854\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin des Sciences Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0007449724001854","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

首先从微分代数的角度研究了第一类和第二类阿贝尔常微分方程。然后利用微分几何证明了第一类阿贝尔常微分方程与曲面上的射影连接之间的关系，使我们能够找到阿贝尔微分方程的“达布第一积分”。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Abel ordinary differential equation, differential algebra and projective connections

We firstly study the Abel ordinary differential equations of the first and second kind from the perspectives of differential algebra. Then using differential geometry we exhibit some relations between the Abel ordinary differential equation of the first kind and projective connections on surfaces which allow us to find a “Darboux first integral” of the Abel differential equation.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊