Kropina Metrics with Isotropic Scalar Curvature via Navigation Data

Yongling Ma, Xiaoling Zhang () and Mengyuan Zhang
Additional contact information
Yongling Ma: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
Xiaoling Zhang: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
Mengyuan Zhang: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China

Mathematics, 2024, vol. 12, issue 4, 1-10

Abstract: Through an interesting physical perspective and a certain contraction of the Ricci curvature tensor in Finsler geometry, Akbar-Zadeh introduced the concept of scalar curvature for the Finsler metric. In this paper, we show that the Kropina metric is of isotropic scalar curvature if and only if F is an Einstein metric according to the navigation data. Moreover, we obtain the three-dimensional rigidity theorem for an Einstein–Kropina metric.

Keywords: Kropina metrics; scalar curvature; Einstein metrics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/4/505/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/4/505/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:4:p:505-:d:1334589

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().