低摩尔斯指数从$S^3$到$S^2$的谐波映射

IF 1.3 1区数学 Q1 MATHEMATICS

Journal of Differential Geometry Pub Date : 2023-09-01 DOI:10.4310/jdg/1695236594

Tristan Rivière

{"title":"低摩尔斯指数从$S^3$到$S^2$的谐波映射","authors":"Tristan Rivière","doi":"10.4310/jdg/1695236594","DOIUrl":null,"url":null,"abstract":"We prove that any smooth harmonic map from $S^3$ into $S^2$ of Morse index less or equal than $4$ has to be an harmonic morphism, that is the successive composition of an isometry of $S^3$, the Hopf fibration and an holomorphic map from $\\mathbb{C}P^1$ into itself.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"42 1","pages":"0"},"PeriodicalIF":1.3000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Harmonic maps from $S^3$ into $S^2$ with low Morse index\",\"authors\":\"Tristan Rivière\",\"doi\":\"10.4310/jdg/1695236594\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that any smooth harmonic map from $S^3$ into $S^2$ of Morse index less or equal than $4$ has to be an harmonic morphism, that is the successive composition of an isometry of $S^3$, the Hopf fibration and an holomorphic map from $\\\\mathbb{C}P^1$ into itself.\",\"PeriodicalId\":15642,\"journal\":{\"name\":\"Journal of Differential Geometry\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Differential Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/jdg/1695236594\",\"RegionNum\":1,\"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":"Journal of Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/jdg/1695236594","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

证明了莫尔斯指数小于或等于$4$的从$S^3$到$S^2$的光滑调和映射必须是调和态射，即$S^3$的等距、Hopf纤维和$\mathbb{C}P^1$到自身的全纯映射的连续复合。

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

Harmonic maps from $S^3$ into $S^2$ with low Morse index

We prove that any smooth harmonic map from $S^3$ into $S^2$ of Morse index less or equal than $4$ has to be an harmonic morphism, that is the successive composition of an isometry of $S^3$, the Hopf fibration and an holomorphic map from $\mathbb{C}P^1$ into itself.

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

Journal of Differential Geometry 数学-数学

CiteScore

3.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes the latest research in differential geometry and related areas of differential equations, mathematical physics, algebraic geometry, and geometric topology.