中性特征四维流形中同调向量场的零点

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2024-05-31 DOI:10.1016/j.geomphys.2024.105239

Graham Hall , Bahar Kırık Rácz

{"title":"中性特征四维流形中同调向量场的零点","authors":"Graham Hall , Bahar Kırık Rácz","doi":"10.1016/j.geomphys.2024.105239","DOIUrl":null,"url":null,"abstract":"<div><p>This paper explores the situation regarding the zeros of a proper homothetic vector field <em>X</em> on a 4-dimensional manifold admitting a metric of neutral signature. The types of such zeros are described in terms of the algebraic types of the Ricci tensor and Weyl tensor at the said zero together with a geometrical description of the set of such zeros. A comparison is made between the situation occurring here and that for positive definite and Lorentz signatures. Examples are given to show that many of the theoretical possibilities derived for such zeros actually exist.</p></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Zeros of homothetic vector fields in 4-dimensional manifolds of neutral signature\",\"authors\":\"Graham Hall , Bahar Kırık Rácz\",\"doi\":\"10.1016/j.geomphys.2024.105239\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper explores the situation regarding the zeros of a proper homothetic vector field <em>X</em> on a 4-dimensional manifold admitting a metric of neutral signature. The types of such zeros are described in terms of the algebraic types of the Ricci tensor and Weyl tensor at the said zero together with a geometrical description of the set of such zeros. A comparison is made between the situation occurring here and that for positive definite and Lorentz signatures. Examples are given to show that many of the theoretical possibilities derived for such zeros actually exist.</p></div>\",\"PeriodicalId\":55602,\"journal\":{\"name\":\"Journal of Geometry and Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Geometry and Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0393044024001402\",\"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":"Journal of Geometry and Physics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0393044024001402","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文探讨了在接纳中性度量的四维流形上的适当同调向量场 X 的零点情况。本文根据在所述零点处的里奇张量和韦尔张量的代数类型来描述这些零点的类型，并对这些零点的集合进行了几何描述。将这里出现的情况与正定符号和洛伦兹符号的情况进行了比较。并举例说明，从理论上推导出的这种零点的许多可能性实际上是存在的。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Zeros of homothetic vector fields in 4-dimensional manifolds of neutral signature

This paper explores the situation regarding the zeros of a proper homothetic vector field X on a 4-dimensional manifold admitting a metric of neutral signature. The types of such zeros are described in terms of the algebraic types of the Ricci tensor and Weyl tensor at the said zero together with a geometrical description of the set of such zeros. A comparison is made between the situation occurring here and that for positive definite and Lorentz signatures. Examples are given to show that many of the theoretical possibilities derived for such zeros actually exist.

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 Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity

期刊最新文献

Editorial Board On conformal collineation and almost Ricci solitons Cohomology and extensions of relative Rota–Baxter groups Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces Complete intersection hyperkähler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one