AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (214.9 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

On some m-th root metrics

Xiaoling Zhang1( ), Cuiling Ma1, Lili Zhao2
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
Show Author Information

Abstract

The Ricci curvature in Finsler geometry naturally generalizes the Ricci curvature in Riemannian geometry. In this paper, we study the m-th root metric with weakly isotropic scalar curvature and obtain that its scalar curvature must vanish. Further, we prove that a locally conformally flat cubic Finsler metric with weakly isotropic scalar curvature must be locally Minkowskian.

Keywords

scalar curvatureweakly isotropic scalar curvaturem-th root Finsler metricslocally conformally flatcubic metrics
CLC number: 53C30, 53C60

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 9 Issue 9,
September 2024
Pages 23971-23978
DOI: 10.3934/math.20241165

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Zhang X, Ma C, Zhao L. On some m-th root metrics. AIMS Mathematics, 2024, 9(9): 23971-23978. https://doi.org/10.3934/math.20241165

94

Views

1

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 16 May 2024
Revised: 26 July 2024
Accepted: 30 July 2024
Published: 15 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)