论球面对称度量的黎曼曲率

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2024-07-27 DOI:10.1007/s11040-024-09486-9

S. G. Elgendi

{"title":"论球面对称度量的黎曼曲率","authors":"S. G. Elgendi","doi":"10.1007/s11040-024-09486-9","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, studying the inverse problem, we establish a curvature compatibility condition on a spherically symmetric Finsler metric. As an application, we characterize the spherically symmetric metrics of scalar curvature. We construct a Berwald frame for a spherically symmetric Finsler surface and calculate some associated geometric objects. Several examples are provided and discussed. Finally, we give a note on a certain general <span>\\((\\alpha ,\\beta )\\)</span>-metric which appears in the literature.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"27 3","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Riemann Curvature of Spherically Symmetric Metrics\",\"authors\":\"S. G. Elgendi\",\"doi\":\"10.1007/s11040-024-09486-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, studying the inverse problem, we establish a curvature compatibility condition on a spherically symmetric Finsler metric. As an application, we characterize the spherically symmetric metrics of scalar curvature. We construct a Berwald frame for a spherically symmetric Finsler surface and calculate some associated geometric objects. Several examples are provided and discussed. Finally, we give a note on a certain general <span>\\\\((\\\\alpha ,\\\\beta )\\\\)</span>-metric which appears in the literature.</p></div>\",\"PeriodicalId\":694,\"journal\":{\"name\":\"Mathematical Physics, Analysis and Geometry\",\"volume\":\"27 3\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-07-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Physics, Analysis and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11040-024-09486-9\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Physics, Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s11040-024-09486-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文在研究逆问题时，建立了球对称芬斯勒度量的曲率相容条件。作为应用，我们描述了标量曲率球对称度量的特征。我们为球面对称 Finsler 曲面构建了一个 Berwald 框架，并计算了一些相关的几何对象。我们还提供并讨论了几个例子。最后，我们对文献中出现的某个一般（(\alpha ,\beta)\）度量作了说明。

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

On Riemann Curvature of Spherically Symmetric Metrics

In this paper, studying the inverse problem, we establish a curvature compatibility condition on a spherically symmetric Finsler metric. As an application, we characterize the spherically symmetric metrics of scalar curvature. We construct a Berwald frame for a spherically symmetric Finsler surface and calculate some associated geometric objects. Several examples are provided and discussed. Finally, we give a note on a certain general \((\alpha ,\beta )\)-metric which appears in the literature.

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

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.